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University of Michigan
1.
Wang, Ting.
Stochastic Analysis of Insurance Products.
Degree: PhD, Applied and Interdisciplinary Mathematics, 2011, University of Michigan
URL: http://hdl.handle.net/2027.42/86347 
► We study the properties of several insurance products via the methods of stochastic analysis and stochastic control. This dissertation consists of the following three parts:…
(more)
▼ We study the properties of several insurance products via the methods of
stochastic analysis and
stochastic control. This dissertation consists of the following three parts:
1. We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset and who can purchase a reversible life annuity. The surrender charge of a life annuity is a proportion of its value. Ruin occurs when the total of the value of the risky and riskless assets and the surrender value of the life annuity reaches zero. We find the optimal investment strategy and optimal annuity purchase and surrender strategies in two situations: (i) the value of the risky and riskless assets is allowed to be negative, with the imputed surrender value of the life annuity keeping the total positive; or (ii) the value of the risky and riskless assets is required to be non-negative.
2. We model a retiree as a utility-maximizing economic agent who can invest in a financial market with a risky and a riskless asset and who can purchase or surrender reversible annuities. We define the wealth of an individual as the total value of her risky and riskless assets, which is required to be non-negative during her lifetime. We solve this incomplete market utility maximization problem via duality arguments and obtain semi-analytical solutions.
3. We develop a theory for pricing pure endowments when hedging with a mortality forward is allowed. The hazard rate associated with the pure endowment and the reference hazard rate for the mortality forward are correlated and are modeled by diffusion processes. We price the pure endowment by assuming that the issuing company hedges its contract with the mortality forward and requires compensation for the unhedgeable part of the mortality risk in the form of a pre-specified instantaneous Sharpe ratio. We identify the properties of the prices of pure endowments and the factors that affect hedging efficiency.
Advisors/Committee Members: Li, Haitao (committee member), Young, Virginia R. (committee member), Bayraktar, Erhan (committee member), Moore, Kristen S. (committee member).
Subjects/Keywords: Stochastic Analysis; Science
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APA (6th Edition):
Wang, T. (2011). Stochastic Analysis of Insurance Products. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/86347
Chicago Manual of Style (16th Edition):
Wang, Ting. “Stochastic Analysis of Insurance Products.” 2011. Doctoral Dissertation, University of Michigan. Accessed March 06, 2021.
http://hdl.handle.net/2027.42/86347.
MLA Handbook (7th Edition):
Wang, Ting. “Stochastic Analysis of Insurance Products.” 2011. Web. 06 Mar 2021.
Vancouver:
Wang T. Stochastic Analysis of Insurance Products. [Internet] [Doctoral dissertation]. University of Michigan; 2011. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/2027.42/86347.
Council of Science Editors:
Wang T. Stochastic Analysis of Insurance Products. [Doctoral Dissertation]. University of Michigan; 2011. Available from: http://hdl.handle.net/2027.42/86347
University of Johannesburg
2.
Kingon, Ian Grenville Douglas.
Configuration planning on an ICL computer utilizing a stochastic network analysis package.
Degree: 2014, University of Johannesburg
URL: http://hdl.handle.net/10210/10634
► M.Sc (Computer Science.)
This dissertation details the implementation of SNAP, a stochastic network analysis package, as the basis of an in-house computer configuration planning facility.…
(more)
▼ M.Sc (Computer Science.)
This dissertation details the implementation of SNAP, a stochastic network analysis package, as the basis of an in-house computer configuration planning facility. The work was performed at Head Office, Gold Fields of South Africa Limited, Johannesburg, South Africa (GFSA) during the period April 1980 to December 1981. SNAP was developed by the Institute of Applied Computer Science at the University of Stellenbosch, Stellenbosch, South Africa. The implementation of SNAP at GFSA signalled the first in-house SNAP facility, and the first SNAP implementation on an ICL computer (although implementation had been in progress at another ICL site since 1979). Although this dissertation is very specific in nature, it is intended to provide an insight into the methodology employed in planning and implementing an in-house configuration planning facility. An overview of multiclass queueing network models and the SNAP package is provided, although no attempt is made to explain the stochastic theory of queueing networks in any detail. Attention is thereafter focussed on the various phases of the project. Problems were encountered in monitoring performance data, and these are looked at in some depth. The question of workload characterization and the difficulties of producing a satisfactory GFSA classification strategy are then presented. The model design, calibration and validation stages are explained using the GFSA model. Thereafter, use of the model for prediction purposes is illustrated by means of a number of examples. Finally, tne memory management model is discussed - main memory does not form part of the SNAP model and has to be dealt with as a separate issue.
Subjects/Keywords: Stochastic network analysis
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APA (6th Edition):
Kingon, I. G. D. (2014). Configuration planning on an ICL computer utilizing a stochastic network analysis package. (Thesis). University of Johannesburg. Retrieved from http://hdl.handle.net/10210/10634
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Kingon, Ian Grenville Douglas. “Configuration planning on an ICL computer utilizing a stochastic network analysis package.” 2014. Thesis, University of Johannesburg. Accessed March 06, 2021.
http://hdl.handle.net/10210/10634.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Kingon, Ian Grenville Douglas. “Configuration planning on an ICL computer utilizing a stochastic network analysis package.” 2014. Web. 06 Mar 2021.
Vancouver:
Kingon IGD. Configuration planning on an ICL computer utilizing a stochastic network analysis package. [Internet] [Thesis]. University of Johannesburg; 2014. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/10210/10634.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Kingon IGD. Configuration planning on an ICL computer utilizing a stochastic network analysis package. [Thesis]. University of Johannesburg; 2014. Available from: http://hdl.handle.net/10210/10634
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Oregon State University
3.
McArthur, Richard D.
Parameter estimation in stochastic multicompartment models with destructive sampling.
Degree: PhD, Statistics, 1981, Oregon State University
URL: http://hdl.handle.net/1957/42099
► In many experimental situations involving compartmental models, a more realistic model is obtained if the rate constants are regarded as random variables. We consider the…
(more)
▼ In many experimental situations involving compartmental models,
a more realistic model is obtained if the rate constants are regarded
as random variables. We consider the problem of estimating the means
and variances of the rate constants in a
stochastic compartmental
model when
a) a time series of observations of an individual system cannot
be made (because of destructive sampling), and
b) exact expressions for the moments of the
stochastic model cannot
be found (as is the case with most multicompartment models).
Several estimation procedures will be described and compared using.
simulated experimental data from three different two-compartment pharmacokinetic
models. While all the procedures -seem to give reasonable
estimates of the means, good estimates of the variances are obtained
only if the covariance structure of the
stochastic model is taken into
account. In addition, the results suggest that the difference between
the mean of the
stochastic model and the deterministic model evaluated
at the means of the rate constants is not as important in the parameter
estimation problem as has been suggested by previous authors.
Advisors/Committee Members: Lindstrom, F. Tom (advisor).
Subjects/Keywords: Stochastic analysis
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APA (6th Edition):
McArthur, R. D. (1981). Parameter estimation in stochastic multicompartment models with destructive sampling. (Doctoral Dissertation). Oregon State University. Retrieved from http://hdl.handle.net/1957/42099
Chicago Manual of Style (16th Edition):
McArthur, Richard D. “Parameter estimation in stochastic multicompartment models with destructive sampling.” 1981. Doctoral Dissertation, Oregon State University. Accessed March 06, 2021.
http://hdl.handle.net/1957/42099.
MLA Handbook (7th Edition):
McArthur, Richard D. “Parameter estimation in stochastic multicompartment models with destructive sampling.” 1981. Web. 06 Mar 2021.
Vancouver:
McArthur RD. Parameter estimation in stochastic multicompartment models with destructive sampling. [Internet] [Doctoral dissertation]. Oregon State University; 1981. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/1957/42099.
Council of Science Editors:
McArthur RD. Parameter estimation in stochastic multicompartment models with destructive sampling. [Doctoral Dissertation]. Oregon State University; 1981. Available from: http://hdl.handle.net/1957/42099
Texas A&M University
4.
Preciado Arreola, Jose Luis.
Functional Estimator Selection Techniques for Production Functions and Frontiers.
Degree: PhD, Industrial Engineering, 2016, Texas A&M University
URL: http://hdl.handle.net/1969.1/174230
► This dissertation provides frameworks to select production function estimators in both the state-contingent and the general monotonic and concave cases. It first presents a Birth-Death…
(more)
▼ This dissertation provides frameworks to select production function estimators in both the state-contingent and the general monotonic and concave cases. It first presents a Birth-Death Markov Chain Monte Carlo (BDMCMC) Bayesian algorithm to endogenously estimate the number of previously unobserved states of nature for a state-contingent frontier. Secondly, it contains a Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm to determine a parsimonious piecewise linear description of a multiplicative monotonic and concave production frontier. The RJMCMC based algorithm is the first computationally efficient one-stage estimator of production frontiers with potentially heteroscedastic inefficiency distribution and environmental variables. Thirdly, it provides general framework, based on machine learning concepts, repeated learning-testing and parametric bootstrapping techniques, to select the best monotonic and concave functional estimator for a production function from a pool of functional estimators. This framework is the first to test potentially nonlinear production function estimators on actual datasets, rather than extrapolation of Monte Carlo simulation results.
Advisors/Committee Members: Johnson, Andrew L (advisor), Ding, Yu (committee member), Bhattacharya, Anirban (committee member), Gautam, Natarajan (committee member).
Subjects/Keywords: model selection; Stochastic Frontier Analysis
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APA ·
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APA (6th Edition):
Preciado Arreola, J. L. (2016). Functional Estimator Selection Techniques for Production Functions and Frontiers. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/174230
Chicago Manual of Style (16th Edition):
Preciado Arreola, Jose Luis. “Functional Estimator Selection Techniques for Production Functions and Frontiers.” 2016. Doctoral Dissertation, Texas A&M University. Accessed March 06, 2021.
http://hdl.handle.net/1969.1/174230.
MLA Handbook (7th Edition):
Preciado Arreola, Jose Luis. “Functional Estimator Selection Techniques for Production Functions and Frontiers.” 2016. Web. 06 Mar 2021.
Vancouver:
Preciado Arreola JL. Functional Estimator Selection Techniques for Production Functions and Frontiers. [Internet] [Doctoral dissertation]. Texas A&M University; 2016. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/1969.1/174230.
Council of Science Editors:
Preciado Arreola JL. Functional Estimator Selection Techniques for Production Functions and Frontiers. [Doctoral Dissertation]. Texas A&M University; 2016. Available from: http://hdl.handle.net/1969.1/174230
Oregon State University
5.
Lin, Huan.
Stochastic analysis of a nonlinear ocean structural system.
Degree: PhD, Civil Engineering, 1994, Oregon State University
URL: http://hdl.handle.net/1957/35512
► Stochastic analysis procedures have been recently applied to analyze nonlinear dynamical systems. In this study, nonlinear responses, stochastic and/or chaotic, are examined and interpreted from…
(more)
▼ Stochastic analysis procedures have been recently applied to analyze nonlinear
dynamical systems. In this study, nonlinear responses,
stochastic and/or chaotic, are
examined and interpreted from a probabilistic perspective. A multi-point-moored
ocean structural system under regular and irregular wave excitations is analytically
examined via a generalized
stochastic Melnikov function and Markov process
approach. Time domain simulations and associated experimental observations are
employed to assist in the interpretation of the analytical predictions.
Taking into account the presence of random noise, a generalized
stochastic
Melnikov function associated with the corresponding averaged system, where a
homoclinic connection exists near the primary resonance, is derived. The effects of
random noise on the boundary of regions of possible existence of chaotic response
is demonstrated via a mean-squared Melnikov criterion.
The random wave field is approximated as random perturbations on regular
and nearly regular (with very narrow-band spectrum) waves by adding a white noise
component, or using a filtered white noise process to fit the JONSWAP spectrum.
A Markov process approach is then applied explicitly to analyze the response.
The evolution of the probability density function (PDF) of nonlinear
stochastic
response under the Markov process approach is characterized by a deterministic
partial differential equation called the Fokker-Planck equation, which in this study is
solved by a path integral solution procedure. Numerical evaluation of the path
integral solution is based on path sum, and the short-time propagator is discretized
accordingly. Short-time propagation is performed by using a fourth order Runge-Kutta scheme to calculate the most probable (i.e. mean) position in the phase space
and to establish the fact that discrete contributions to the random response are locally
Gaussian. Transient and steady-state PDF's can be obtained by repeat application of
the short-time propagation.
Based on depictions of the joint probability density functions and time domain
simulations, it is observed that the presence of random noise may expedite the
occurrence of "noisy" chaotic response. The noise intensity governs the transition
among various types of
stochastic nonlinear responses and the relative strengths of
coexisting response attractors. Experimental observations confirm the general
behavior depicted by the analytical predictions.
Advisors/Committee Members: Yim, Solomon C. S. (advisor), Burton, Robert M. (committee member).
Subjects/Keywords: Stochastic analysis
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APA ·
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Manager
APA (6th Edition):
Lin, H. (1994). Stochastic analysis of a nonlinear ocean structural system. (Doctoral Dissertation). Oregon State University. Retrieved from http://hdl.handle.net/1957/35512
Chicago Manual of Style (16th Edition):
Lin, Huan. “Stochastic analysis of a nonlinear ocean structural system.” 1994. Doctoral Dissertation, Oregon State University. Accessed March 06, 2021.
http://hdl.handle.net/1957/35512.
MLA Handbook (7th Edition):
Lin, Huan. “Stochastic analysis of a nonlinear ocean structural system.” 1994. Web. 06 Mar 2021.
Vancouver:
Lin H. Stochastic analysis of a nonlinear ocean structural system. [Internet] [Doctoral dissertation]. Oregon State University; 1994. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/1957/35512.
Council of Science Editors:
Lin H. Stochastic analysis of a nonlinear ocean structural system. [Doctoral Dissertation]. Oregon State University; 1994. Available from: http://hdl.handle.net/1957/35512
University of Oxford
6.
Nejad, Sina.
Lipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacian.
Degree: PhD, 2018, University of Oxford
URL: http://ora.ox.ac.uk/objects/uuid:5805be09-93e5-4f18-b960-732f81f85860
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.780422
► This thesis is a tale of two halves. The first introduces the space of unparameterised geometric rough paths and develops a notion of Lipschitz function…
(more)
▼ This thesis is a tale of two halves. The first introduces the space of unparameterised geometric rough paths and develops a notion of Lipschitz function on this space. The second associates an expected signature to the bilaplacian and culminates in an analogue of the Feynman-Kac formula for high-order parabolic partial differential equations.
Subjects/Keywords: Rough paths; Stochastic analysis
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APA ·
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APA (6th Edition):
Nejad, S. (2018). Lipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacian. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:5805be09-93e5-4f18-b960-732f81f85860 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.780422
Chicago Manual of Style (16th Edition):
Nejad, Sina. “Lipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacian.” 2018. Doctoral Dissertation, University of Oxford. Accessed March 06, 2021.
http://ora.ox.ac.uk/objects/uuid:5805be09-93e5-4f18-b960-732f81f85860 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.780422.
MLA Handbook (7th Edition):
Nejad, Sina. “Lipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacian.” 2018. Web. 06 Mar 2021.
Vancouver:
Nejad S. Lipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacian. [Internet] [Doctoral dissertation]. University of Oxford; 2018. [cited 2021 Mar 06].
Available from: http://ora.ox.ac.uk/objects/uuid:5805be09-93e5-4f18-b960-732f81f85860 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.780422.
Council of Science Editors:
Nejad S. Lipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacian. [Doctoral Dissertation]. University of Oxford; 2018. Available from: http://ora.ox.ac.uk/objects/uuid:5805be09-93e5-4f18-b960-732f81f85860 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.780422
Michigan State University
7.
Liu, Rui.
The asymptotic behavior of stochastic evolution equations.
Degree: PhD, Department of Mathematics, 1996, Michigan State University
URL: http://etd.lib.msu.edu/islandora/object/etd:26164
Subjects/Keywords: Stochastic analysis
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APA ·
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APA (6th Edition):
Liu, R. (1996). The asymptotic behavior of stochastic evolution equations. (Doctoral Dissertation). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:26164
Chicago Manual of Style (16th Edition):
Liu, Rui. “The asymptotic behavior of stochastic evolution equations.” 1996. Doctoral Dissertation, Michigan State University. Accessed March 06, 2021.
http://etd.lib.msu.edu/islandora/object/etd:26164.
MLA Handbook (7th Edition):
Liu, Rui. “The asymptotic behavior of stochastic evolution equations.” 1996. Web. 06 Mar 2021.
Vancouver:
Liu R. The asymptotic behavior of stochastic evolution equations. [Internet] [Doctoral dissertation]. Michigan State University; 1996. [cited 2021 Mar 06].
Available from: http://etd.lib.msu.edu/islandora/object/etd:26164.
Council of Science Editors:
Liu R. The asymptotic behavior of stochastic evolution equations. [Doctoral Dissertation]. Michigan State University; 1996. Available from: http://etd.lib.msu.edu/islandora/object/etd:26164
University of Hong Kong
8.
曾慧賢.
Aspects of modelling
stochastic volatility.
Degree: 2000, University of Hong Kong
URL: http://hdl.handle.net/10722/33457
Subjects/Keywords: Stochastic analysis.
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APA ·
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APA (6th Edition):
曾慧賢. (2000). Aspects of modelling
stochastic volatility. (Thesis). University of Hong Kong. Retrieved from http://hdl.handle.net/10722/33457
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
曾慧賢. “Aspects of modelling
stochastic volatility.” 2000. Thesis, University of Hong Kong. Accessed March 06, 2021.
http://hdl.handle.net/10722/33457.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
曾慧賢. “Aspects of modelling
stochastic volatility.” 2000. Web. 06 Mar 2021.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Vancouver:
曾慧賢. Aspects of modelling
stochastic volatility. [Internet] [Thesis]. University of Hong Kong; 2000. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/10722/33457.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
曾慧賢. Aspects of modelling
stochastic volatility. [Thesis]. University of Hong Kong; 2000. Available from: http://hdl.handle.net/10722/33457
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation
University of Colorado
9.
Zhou, Dingyu.
Global Sensitivity and Stochastic Pathway Analysis of Chemical Mechanisms.
Degree: PhD, Chemistry & Biochemistry, 2012, University of Colorado
URL: https://scholar.colorado.edu/chem_gradetds/84
► The use of theoretical kinetic modeling provides an invaluable tool for the study of biofuel blend development and optimization. These models provide a way…
(more)
▼ The use of theoretical kinetic modeling provides an invaluable tool for the study of biofuel blend development and optimization. These models provide a way to simulate complex combustion systems and extract information without the need for costly experimental procedures. Indeed, these models often allow one to treat extreme conditions, such as those found in combustion engines, where in situ experiment is not yet feasible. However, many combustion models have large uncertainties in their rate coefficients and many models have been optimized for just a few specific conditions. Therefore, systematic improvement of biofuel combustion models is often necessary. Since these models are quite large, for example the n-butanol combustion mechanism contains 1446 reactions and 243 species, a brute force improvement all rate constant parameters is practically impossible. My Ph.D. work involved applying a global sensitivity
analysis (GSA) method to combustion models of biofuel components in order to identify and improve the rate constants within the mechanisms that had the largest effect on the target simulation result. Specifically, my main focus was the combustion of n-butanol. GSA revealed that a target simulation result, the ignition time delay, was quite sensitive to self-reaction of the hydroperoxy radical HO2+HO2->H2O2+O2. The empirical rate coefficient for this reaction had a large uncertainty; therefore, high level ab initio calculations and transition state theory were used to calculate a more accurate rate coefficient for this reaction. The second part of my Ph.D. study involved developing an efficient method for determining the pathways taken during a chemical process using a
stochastic method that followed ¡§single atoms¡¨. This study was motivated with the intent of extending the GSA method to account not only for the sensitivity of simulation results to single reactions, but to entire chemical pathways. The method I developed extracts not only reaction flow within the chemical network, but specifies the probabilities of exact chemical pathways.
Advisors/Committee Members: Rex T. Skodje, Robert Parson, Joel Eaves, Veronica Vaida, J. Will Medlin.
Subjects/Keywords: Global Sensitivity Analysis; Stochastic Pathway Analysis; Chemistry
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APA (6th Edition):
Zhou, D. (2012). Global Sensitivity and Stochastic Pathway Analysis of Chemical Mechanisms. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/chem_gradetds/84
Chicago Manual of Style (16th Edition):
Zhou, Dingyu. “Global Sensitivity and Stochastic Pathway Analysis of Chemical Mechanisms.” 2012. Doctoral Dissertation, University of Colorado. Accessed March 06, 2021.
https://scholar.colorado.edu/chem_gradetds/84.
MLA Handbook (7th Edition):
Zhou, Dingyu. “Global Sensitivity and Stochastic Pathway Analysis of Chemical Mechanisms.” 2012. Web. 06 Mar 2021.
Vancouver:
Zhou D. Global Sensitivity and Stochastic Pathway Analysis of Chemical Mechanisms. [Internet] [Doctoral dissertation]. University of Colorado; 2012. [cited 2021 Mar 06].
Available from: https://scholar.colorado.edu/chem_gradetds/84.
Council of Science Editors:
Zhou D. Global Sensitivity and Stochastic Pathway Analysis of Chemical Mechanisms. [Doctoral Dissertation]. University of Colorado; 2012. Available from: https://scholar.colorado.edu/chem_gradetds/84
University of Oxford
10.
Foster, James Matthew.
Numerical approximations for stochastic differential equations.
Degree: PhD, 2020, University of Oxford
URL: http://ora.ox.ac.uk/objects/uuid:775fc3f5-501c-425f-8b43-fc5a7b2e4310
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.820760
► In this thesis, we consider problems related to the numerical simulation of stochastic differential equations (SDEs). In particular, we are interested in methods that use…
(more)
▼ In this thesis, we consider problems related to the numerical simulation of stochastic differential equations (SDEs). In particular, we are interested in methods that use both increments and areas of the Brownian path. For example, time integrals of Brownian motion carry useful information whilst being normally distributed and thus straightforward to generate. We will make precise the "path information" contained by such integrals and present a polynomial approximation theorem for Brownian motion. Since the Gaussian coefficients given by this expansion are independent, we can express Brownian motion as a polynomial with additional noise. We shall then use this simple observation to develop high order methods. The majority of these methods approximate SDEs through the use of ODEs, which can be accurately discretized using state-of-the-art solvers. To numerically demonstrate these approaches, we will simulate four SDEs: Inhomogeneous Geometric Brownian Motion, Cox-Ingersoll-Ross model, underdamped Langevin equation and the Lévy area of Brownian motion. The code for these examples can be found at github.com/james-m-foster. We also study problems related to variable step size methods for SDEs. Most notably, we investigate which numerical methods and variable step size strategies can ensure pathwise convergence to the true SDE solution. Our analysis is based on rough path theory and requires methods to be locally close to an ODE driven by a piecewise "Brownian polynomial". This result can therefore be applied to the Heun and midpoint methods. In order to prove convergence, we will require variable step size strategies to produce a nested sequence of partitions with mesh size tending to zero.
Subjects/Keywords: Rough path theory; Numerical analysis; Stochastic analysis
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APA (6th Edition):
Foster, J. M. (2020). Numerical approximations for stochastic differential equations. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:775fc3f5-501c-425f-8b43-fc5a7b2e4310 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.820760
Chicago Manual of Style (16th Edition):
Foster, James Matthew. “Numerical approximations for stochastic differential equations.” 2020. Doctoral Dissertation, University of Oxford. Accessed March 06, 2021.
http://ora.ox.ac.uk/objects/uuid:775fc3f5-501c-425f-8b43-fc5a7b2e4310 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.820760.
MLA Handbook (7th Edition):
Foster, James Matthew. “Numerical approximations for stochastic differential equations.” 2020. Web. 06 Mar 2021.
Vancouver:
Foster JM. Numerical approximations for stochastic differential equations. [Internet] [Doctoral dissertation]. University of Oxford; 2020. [cited 2021 Mar 06].
Available from: http://ora.ox.ac.uk/objects/uuid:775fc3f5-501c-425f-8b43-fc5a7b2e4310 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.820760.
Council of Science Editors:
Foster JM. Numerical approximations for stochastic differential equations. [Doctoral Dissertation]. University of Oxford; 2020. Available from: http://ora.ox.ac.uk/objects/uuid:775fc3f5-501c-425f-8b43-fc5a7b2e4310 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.820760
Western Kentucky University
11.
Cheng, Gang.
Analyzing and Solving Non-Linear Stochastic Dynamic Models on Non-Periodic Discrete Time Domains.
Degree: MS, Department of Mathematics, 2013, Western Kentucky University
URL: https://digitalcommons.wku.edu/theses/1236
► Stochastic dynamic programming is a recursive method for solving sequential or multistage decision problems. It helps economists and mathematicians construct and solve a huge…
(more)
▼ Stochastic dynamic programming is a recursive method for solving sequential or multistage decision problems. It helps economists and mathematicians construct and solve a huge variety of sequential decision making problems in
stochastic cases. Research on
stochastic dynamic programming is important and meaningful because
stochastic dynamic programming reflects the behavior of the decision maker without risk aversion; i.e., decision making under uncertainty. In the solution process, it is extremely difficult to represent the existing or future state precisely since uncertainty is a state of having limited knowledge. Indeed, compared to the deterministic case, which is decision making under certainty, the
stochastic case is more realistic and gives more accurate results because the majority of problems in reality inevitably have many unknown parameters. In addition, time scale calculus theory is applicable to any field in which a dynamic process can be described with discrete or continuous models. Many
stochastic dynamic models are discrete or continuous, so the results of time scale calculus are directly applicable to them as well. The aim of this thesis is to introduce a general form of a
stochastic dynamic sequence problem on complex discrete time domains and to find the optimal sequence which maximizes the sequence problem.
Advisors/Committee Members: Ferhan Atici (Director), Tom Richmond, Di Wu.
Subjects/Keywords: Dynamic Programming; Stochastic Programming; Stochastic Control Theory; Stochastic Differential Equations; Stochastic Analysis; Martingales (Mathematics); Analysis; Applied Mathematics; Mathematics; Statistics and Probability
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APA (6th Edition):
Cheng, G. (2013). Analyzing and Solving Non-Linear Stochastic Dynamic Models on Non-Periodic Discrete Time Domains. (Masters Thesis). Western Kentucky University. Retrieved from https://digitalcommons.wku.edu/theses/1236
Chicago Manual of Style (16th Edition):
Cheng, Gang. “Analyzing and Solving Non-Linear Stochastic Dynamic Models on Non-Periodic Discrete Time Domains.” 2013. Masters Thesis, Western Kentucky University. Accessed March 06, 2021.
https://digitalcommons.wku.edu/theses/1236.
MLA Handbook (7th Edition):
Cheng, Gang. “Analyzing and Solving Non-Linear Stochastic Dynamic Models on Non-Periodic Discrete Time Domains.” 2013. Web. 06 Mar 2021.
Vancouver:
Cheng G. Analyzing and Solving Non-Linear Stochastic Dynamic Models on Non-Periodic Discrete Time Domains. [Internet] [Masters thesis]. Western Kentucky University; 2013. [cited 2021 Mar 06].
Available from: https://digitalcommons.wku.edu/theses/1236.
Council of Science Editors:
Cheng G. Analyzing and Solving Non-Linear Stochastic Dynamic Models on Non-Periodic Discrete Time Domains. [Masters Thesis]. Western Kentucky University; 2013. Available from: https://digitalcommons.wku.edu/theses/1236
Georgia Tech
12.
Ramos, José A.
A stochastic realization and model reduction approach to streamflow modeling.
Degree: PhD, Civil engineering, 1985, Georgia Tech
URL: http://hdl.handle.net/1853/32869
Subjects/Keywords: Stochastic processes; Stochastic analysis
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Chicago ·
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APA (6th Edition):
Ramos, J. A. (1985). A stochastic realization and model reduction approach to streamflow modeling. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/32869
Chicago Manual of Style (16th Edition):
Ramos, José A. “A stochastic realization and model reduction approach to streamflow modeling.” 1985. Doctoral Dissertation, Georgia Tech. Accessed March 06, 2021.
http://hdl.handle.net/1853/32869.
MLA Handbook (7th Edition):
Ramos, José A. “A stochastic realization and model reduction approach to streamflow modeling.” 1985. Web. 06 Mar 2021.
Vancouver:
Ramos JA. A stochastic realization and model reduction approach to streamflow modeling. [Internet] [Doctoral dissertation]. Georgia Tech; 1985. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/1853/32869.
Council of Science Editors:
Ramos JA. A stochastic realization and model reduction approach to streamflow modeling. [Doctoral Dissertation]. Georgia Tech; 1985. Available from: http://hdl.handle.net/1853/32869
Rutgers University
13.
Goschin, Sergiu, 1980-.
Stochastic dilemmas: foundations and applications.
Degree: Computer Science, 2014, Rutgers University
URL: https://rucore.libraries.rutgers.edu/rutgers-lib/44107/
Subjects/Keywords: Stochastic processes; Stochastic analysis
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to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Goschin, Sergiu, 1. (2014). Stochastic dilemmas: foundations and applications. (Thesis). Rutgers University. Retrieved from https://rucore.libraries.rutgers.edu/rutgers-lib/44107/
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Goschin, Sergiu, 1980-. “Stochastic dilemmas: foundations and applications.” 2014. Thesis, Rutgers University. Accessed March 06, 2021.
https://rucore.libraries.rutgers.edu/rutgers-lib/44107/.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Goschin, Sergiu, 1980-. “Stochastic dilemmas: foundations and applications.” 2014. Web. 06 Mar 2021.
Vancouver:
Goschin, Sergiu 1. Stochastic dilemmas: foundations and applications. [Internet] [Thesis]. Rutgers University; 2014. [cited 2021 Mar 06].
Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/44107/.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Goschin, Sergiu 1. Stochastic dilemmas: foundations and applications. [Thesis]. Rutgers University; 2014. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/44107/
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Oxford
14.
Lionnet, Arnaud.
Topics on backward stochastic differential equations : theoretical and practical aspects.
Degree: PhD, 2013, University of Oxford
URL: http://ora.ox.ac.uk/objects/uuid:0c1154d0-61ac-428a-8ef7-29a546f2da42
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.595938
► This doctoral thesis is concerned with some theoretical and practical questions related to backward stochastic differential equations (BSDEs) and more specifically their connection with some…
(more)
▼ This doctoral thesis is concerned with some theoretical and practical questions related to backward stochastic differential equations (BSDEs) and more specifically their connection with some parabolic partial differential equations (PDEs). The thesis is made of three parts. In the first part, we study the probabilistic representation for a class of multidimensional PDEs with quadratic nonlinearities of a special form. We obtain a representation formula for the PDE solution in terms of the solutions to a Lipschitz BSDE. We then use this representation to obtain an estimate on the gradient of the PDE solutions by probabilistic means. In the course of our analysis, we are led to prove some results for the associated multidimensional quadratic BSDEs, namely an existence result and a partial uniqueness result. In the second part, we study the well-posedness of a very general quadratic reflected BSDE driven by a continuous martingale. We obtain the comparison theorem, the special comparison theorem for reflected BSDEs (which allows to compare the increasing processes of two solutions), the uniqueness and existence of solutions, as well as a stability result. The comparison theorem (from which uniqueness follows) and the special comparison theorem are obtained through natural techniques and minimal assumptions. The existence is based on a perturbative procedure, and holds for a driver whis is Lipschitz, or slightly-superlinear, or monotone with arbitrary growth in y. Finally, we obtain a stability result, which gives in particular a local Lipschitz estimate in BMO for the martingale part of the solution. In the third and last part, we study the time-discretization of BSDEs having nonlinearities that are monotone but with polynomial growth in the primary variable. We show that in that case, the explicit Euler scheme is likely to diverge, while the implicit scheme converges. In fact, by studying the family of θ-schemes, which are mixed explicit-implicit, θ characterizing the degree of implicitness, we find that the scheme converges when the implicit component is dominant (θ ≥ 1/2 ). We then propose a tamed explicit scheme, which converges. We show that the implicit-dominant schemes with θ > 1/2 and our tamed explicit scheme converge with order 1/2 , while the trapezoidal scheme (θ = 1/2) converges with order 7/4.
Subjects/Keywords: 519.2; Mathematics; Probability theory and stochastic processes; stochastic analysis; stochastic processes; martingales; backward stochastic differential equations; Feynman-Kac formula; numerical methods
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APA (6th Edition):
Lionnet, A. (2013). Topics on backward stochastic differential equations : theoretical and practical aspects. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:0c1154d0-61ac-428a-8ef7-29a546f2da42 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.595938
Chicago Manual of Style (16th Edition):
Lionnet, Arnaud. “Topics on backward stochastic differential equations : theoretical and practical aspects.” 2013. Doctoral Dissertation, University of Oxford. Accessed March 06, 2021.
http://ora.ox.ac.uk/objects/uuid:0c1154d0-61ac-428a-8ef7-29a546f2da42 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.595938.
MLA Handbook (7th Edition):
Lionnet, Arnaud. “Topics on backward stochastic differential equations : theoretical and practical aspects.” 2013. Web. 06 Mar 2021.
Vancouver:
Lionnet A. Topics on backward stochastic differential equations : theoretical and practical aspects. [Internet] [Doctoral dissertation]. University of Oxford; 2013. [cited 2021 Mar 06].
Available from: http://ora.ox.ac.uk/objects/uuid:0c1154d0-61ac-428a-8ef7-29a546f2da42 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.595938.
Council of Science Editors:
Lionnet A. Topics on backward stochastic differential equations : theoretical and practical aspects. [Doctoral Dissertation]. University of Oxford; 2013. Available from: http://ora.ox.ac.uk/objects/uuid:0c1154d0-61ac-428a-8ef7-29a546f2da42 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.595938
University of Rochester
15.
Zeng, Yan (1987 - ).
Blow-up results for stochastic heat equations.
Degree: PhD, 2013, University of Rochester
URL: http://hdl.handle.net/1802/27178
► Consider the stochastic partial dierential equation <i>ut</i> = <i>uxx + g(u)Ẇ</i> where x ∈ <b>I</b> ≡ [0, J], Ẇ = Ẇ(t, x) is 2-parameter white…
(more)
▼ Consider the stochastic partial dierential equation
<i>ut</i> =
<i>uxx + g(u)Ẇ</i>
where x ∈ <b>I</b> ≡ [0, J], Ẇ = Ẇ(t,
x) is 2-parameter white noise, and we assume the initial function
u(0, x) is nonnegative and not identically 0. We impose
Dirichlet
boundary conditions on u in <b>I</b>. We say u blows up
in finite time, with
positive probability, if there is a random
time T < ∞ such that [Formula would not render]
Let
g(u) = u<sup>γ</sup>. It was already known that
if γ < 3/2 , then u does not blow up in
finite time
almost surely. It has also been proved by Carl Mueller in [4] that
there
is a positive probability that u blows up in finite time
when γ > 3=2. However, for the case γ = 3/2 the
problem is still left open.
In this paper, we
found that when [Formula would not render] the solution does not
blow up in finite time. Moreover, when g(u) =
u3/2(log (u +
1))<sup>α</sup>, the equation will have
positive probability to blow up in finite time. In the last
chapter, we apply
some numerical approximations to our Stochastic
Partial Differential Equation,
which gives us some intuition about
how the solution evolves. Unfortunately, the
scheme we use for the
approximation only has a low convergence rate, which puts
the
effectiveness of numerical simulations in
question.
Subjects/Keywords: Analysis; Blow-up; Probability; Stochastic heat equation
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APA (6th Edition):
Zeng, Y. (. -. ). (2013). Blow-up results for stochastic heat equations. (Doctoral Dissertation). University of Rochester. Retrieved from http://hdl.handle.net/1802/27178
Chicago Manual of Style (16th Edition):
Zeng, Yan (1987 - ). “Blow-up results for stochastic heat equations.” 2013. Doctoral Dissertation, University of Rochester. Accessed March 06, 2021.
http://hdl.handle.net/1802/27178.
MLA Handbook (7th Edition):
Zeng, Yan (1987 - ). “Blow-up results for stochastic heat equations.” 2013. Web. 06 Mar 2021.
Vancouver:
Zeng Y(-). Blow-up results for stochastic heat equations. [Internet] [Doctoral dissertation]. University of Rochester; 2013. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/1802/27178.
Council of Science Editors:
Zeng Y(-). Blow-up results for stochastic heat equations. [Doctoral Dissertation]. University of Rochester; 2013. Available from: http://hdl.handle.net/1802/27178
16.
Lamontagne, Jonathan.
Representation Of Uncertainty And Corridor Dp For Hydropower Optimization.
Degree: PhD, Civil and Environmental Engineering, 2015, Cornell University
URL: http://hdl.handle.net/1813/39482
► This thesis focuses on optimization techniques for multi-reservoir hydropower systems operation, with a particular concern with the representation and impact of uncertainty. The thesis reports…
(more)
▼ This thesis focuses on optimization techniques for multi-reservoir hydropower systems operation, with a particular concern with the representation and impact of uncertainty. The thesis reports on three research investigations: 1) examination of the impact of uncertainty representations, 2) efficient solution methods for multi-reservoir
stochastic dynamic programming (SDP) models, and 3) diagnostic analyses for hydropower system operation. The first investigation explores the value of sophistication in the representation of forecast and inflow uncertainty in
stochastic hydropower optimization models using a sampling SDP (SSDP) model framework. SSDP models with different uncertainty representation ranging in sophistication from simple deterministic to complex dynamic
stochastic models are employed when optimize a single reservoir systems [similar to Faber and Stedinger, 2001]. The effect of uncertainty representation on simulated system performance is examined with varying storage and powerhouse capacity, and with random or mean energy prices. In many cases very simple uncertainty models perform as well as more complex ones, but not always. The second investigation develops a new and efficient algorithm for solving multi-reservoir SDP models: Corridor SDP. Rather than employing a uniform grid across the entire state space, Corridor SDP efficiently concentrates points in where the system is likely to visit, as determined by historical operations or simulation. Radial basis functions (RBFs) are used for interpolation. A greedy algorithm places points where they are needed to achieve a good approximation. In a four-reservoir test case, Corridor DP achieves the same accuracy as spline-DP and linear-DP with approximately 1/10 and 1/1100 the number of discrete points, respectively. When local curvature is more pronounced (due to minimum-flow constraints), Corridor DP achieves the same accuracy as spline-DP and linear-DP with approximately 1/30 and 1/215 the number of points, respectively. The third investigation explores three diagnostic approaches for analyzing hydropower system operation. First, several simple diagnostic statistics describe reservoir volume and powerhouse capacity in units of time, allowing scale-invariant comparisons and classification of different reservoir systems and their operation. Second, a regression
analysis using optimal storage/release sequences identifies the most useful hydrologic state variables . Finally spectral density estimation identifies critical time scales for operation for several single-reservoir systems considering mean and random energy prices. Deregulation of energy markets has made optimization of hydropower operations an active concern. Another development is publication of Extended Streamflow Forecasts (ESP) by the National Weather Service (NWS) and others to describe flow forecasts and their precision; the multivariate Sampling SDP models employed here are appropriately structured to incorporate such information in operational hydropower decisions. This research contributes…
Advisors/Committee Members: Stedinger, Jery Russell (chair), Topaloglu, Huseyin (committee member), Parlange, Jean-Yves (committee member).
Subjects/Keywords: Dynamic Programming; Stochastic Optimization; Uncertainty Analysis
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APA (6th Edition):
Lamontagne, J. (2015). Representation Of Uncertainty And Corridor Dp For Hydropower Optimization. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/39482
Chicago Manual of Style (16th Edition):
Lamontagne, Jonathan. “Representation Of Uncertainty And Corridor Dp For Hydropower Optimization.” 2015. Doctoral Dissertation, Cornell University. Accessed March 06, 2021.
http://hdl.handle.net/1813/39482.
MLA Handbook (7th Edition):
Lamontagne, Jonathan. “Representation Of Uncertainty And Corridor Dp For Hydropower Optimization.” 2015. Web. 06 Mar 2021.
Vancouver:
Lamontagne J. Representation Of Uncertainty And Corridor Dp For Hydropower Optimization. [Internet] [Doctoral dissertation]. Cornell University; 2015. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/1813/39482.
Council of Science Editors:
Lamontagne J. Representation Of Uncertainty And Corridor Dp For Hydropower Optimization. [Doctoral Dissertation]. Cornell University; 2015. Available from: http://hdl.handle.net/1813/39482
Columbia University
17.
Qian, Huajie.
Uncertainty Quantification in Data-Driven Simulation and Optimization: Statistical and Computational Efficiency.
Degree: 2020, Columbia University
URL: https://doi.org/10.7916/d8-mdgf-q478
► Models governing stochasticity in various systems are typically calibrated from data, therefore are subject to statistical errors/uncertainties which can lead to inferior decision making. This…
(more)
▼ Models governing stochasticity in various systems are typically calibrated from data, therefore are subject to statistical errors/uncertainties which can lead to inferior decision making. This thesis develops statistically and computationally efficient data-driven methods for problems in stochastic simulation and optimization to quantify and hedge impacts of these uncertainties.
The first half of the thesis focuses on efficient methods for tackling input uncertainty which refers to the simulation output variability arising from the statistical noise in specifying the input models. Due to the convolution of the simulation noise and the input noise, existing bootstrap approaches consist of a two-layer sampling and typically require substantial simulation effort. Chapter 2 investigates a subsampling framework to reduce the required effort, by leveraging the form of the variance and its estimation error in terms of the data size and the sampling requirement in each layer. We show how the total required effort is reduced, and explicitly identify the procedural specifications in our framework that guarantee relative consistency in the estimation, and the corresponding optimal simulation budget allocations. In Chapter 3 we study an optimization-based approach to construct confidence intervals for simulation outputs under input uncertainty. This approach computes confidence bounds from simulation runs driven by probability weights defined on the data, which are obtained from solving optimization problems under suitably posited averaged divergence constraints. We illustrate how this approach offers benefits in computational efficiency and finite-sample performance compared to the bootstrap and the delta method. While resembling distributionally robust optimization, we explain the procedural design and develop tight statistical guarantees via a generalization of the empirical likelihood method.
The second half develops uncertainty quantification techniques for certifying solution feasibility and optimality in data-driven optimization. Regarding optimality, Chapter 4 proposes a statistical method to estimate the optimality gap of a given solution for stochastic optimization as an assessment of the solution quality. Our approach is based on bootstrap aggregating, or bagging, resampled sample average approximation (SAA). We show how this approach leads to valid statistical confidence bounds for non-smooth optimization. We also demonstrate its statistical efficiency and stability that are especially desirable in limited-data situations. We present our theory that views SAA as a kernel in an infinite-order symmetric statistic. Regarding feasibility, Chapter 5 considers data-driven optimization under uncertain constraints, where solution feasibility is often ensured through a "safe" reformulation of the constraints, such that an obtained solution is guaranteed feasible for the oracle formulation with high confidence. Such approaches generally involve an implicit estimation of the whole feasible set that can scale…
Subjects/Keywords: Operations research; Statistics; Stochastic analysis; Bootstrap (Statistics)
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MLA ·
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Export
to Zotero / EndNote / Reference
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APA (6th Edition):
Qian, H. (2020). Uncertainty Quantification in Data-Driven Simulation and Optimization: Statistical and Computational Efficiency. (Doctoral Dissertation). Columbia University. Retrieved from https://doi.org/10.7916/d8-mdgf-q478
Chicago Manual of Style (16th Edition):
Qian, Huajie. “Uncertainty Quantification in Data-Driven Simulation and Optimization: Statistical and Computational Efficiency.” 2020. Doctoral Dissertation, Columbia University. Accessed March 06, 2021.
https://doi.org/10.7916/d8-mdgf-q478.
MLA Handbook (7th Edition):
Qian, Huajie. “Uncertainty Quantification in Data-Driven Simulation and Optimization: Statistical and Computational Efficiency.” 2020. Web. 06 Mar 2021.
Vancouver:
Qian H. Uncertainty Quantification in Data-Driven Simulation and Optimization: Statistical and Computational Efficiency. [Internet] [Doctoral dissertation]. Columbia University; 2020. [cited 2021 Mar 06].
Available from: https://doi.org/10.7916/d8-mdgf-q478.
Council of Science Editors:
Qian H. Uncertainty Quantification in Data-Driven Simulation and Optimization: Statistical and Computational Efficiency. [Doctoral Dissertation]. Columbia University; 2020. Available from: https://doi.org/10.7916/d8-mdgf-q478
Columbia University
18.
Petromichelakis, Ioannis.
Path integral techniques and Gröbner basis approaches for stochastic response analysis and optimization of diverse nonlinear dynamic systems.
Degree: 2020, Columbia University
URL: https://doi.org/10.7916/d8-6p2s-hr09
► This thesis focuses primarily on generalizations and enhancements of the Wiener path integral (WPI) technique for stochastic response analysis and optimization of diverse nonlinear dynamic…
(more)
▼ This thesis focuses primarily on generalizations and enhancements of the Wiener path integral (WPI) technique for stochastic response analysis and optimization of diverse nonlinear dynamic systems of engineering interest. Concisely, the WPI technique, which has proven to be a potent mathematical tool in theoretical physics, has been recently extended to address problems in stochastic engineering dynamics. Herein, the WPI technique has been significantly enhanced in terms of computational efficiency and versatility; these results are presented in Chapters 2-5.
Specifically, in Chapter 2 a brief introduction to the standard WPI solution approach is outlined. In Chapter 3, a novel methodology is presented, which utilizes theoretical results from calculus of variations to extend the WPI for determining marginalized response PDFs of n-degree-of-freedom (n-DOF) nonlinear systems. The associated computational cost relates to the dimension of the PDF and is essentially independent from the dimension n of the system. In several commonly encountered cases, the aforementioned methodology improves the computational efficiency of the WPI by orders of magnitude, and exhibits a significant advantage over the commonly utilized Monte-Carlo-simulation (MCS). Moreover, in Chapter 4, an extension of the WPI technique is presented for addressing the challenge of determining the stochastic response of nonlinear dynamical systems under the presence of singularities in the diffusion matrix. The key idea behind this approach is to partition the original system into an underdetermined system of SDEs corresponding to a nonsingular diffusion matrix and an underdetermined system of homogeneous differential equations; the latter is treated as a dynamic constraint that allows for employing constrained variational/optimization solution methods. In Chapter 5, this approach is applied for the stochastic response analysis and optimization of electromechanical vibratory energy harvesters.
Next, in Chapter 6, a technique from computational algebraic geometry has been developed, which is based on the concept of Gröbner basis and is capable of determining the entire solution set of systems of polynomial equations. This technique has been utilized to address diverse challenging problems in engineering mechanics. First, after formulating the WPI as a minimization problem, it is shown in Chapter 7 that the corresponding objective function is convex, and thus, convergence of numerical schemes to the global optimum is guaranteed. Second, in Chapter 8, the computational algebraic geometry technique has been applied to the challenging problem of determining nonlinear normal modes (NNMs) corresponding to multi-degree-of-freedom dynamical systems as defined in [1], and has been shown to yield improvements in accuracy compared to the standard treatment in the literature.
Subjects/Keywords: Civil engineering; Mathematics; Stochastic analysis; Nonlinear systems
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Export
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APA (6th Edition):
Petromichelakis, I. (2020). Path integral techniques and Gröbner basis approaches for stochastic response analysis and optimization of diverse nonlinear dynamic systems. (Doctoral Dissertation). Columbia University. Retrieved from https://doi.org/10.7916/d8-6p2s-hr09
Chicago Manual of Style (16th Edition):
Petromichelakis, Ioannis. “Path integral techniques and Gröbner basis approaches for stochastic response analysis and optimization of diverse nonlinear dynamic systems.” 2020. Doctoral Dissertation, Columbia University. Accessed March 06, 2021.
https://doi.org/10.7916/d8-6p2s-hr09.
MLA Handbook (7th Edition):
Petromichelakis, Ioannis. “Path integral techniques and Gröbner basis approaches for stochastic response analysis and optimization of diverse nonlinear dynamic systems.” 2020. Web. 06 Mar 2021.
Vancouver:
Petromichelakis I. Path integral techniques and Gröbner basis approaches for stochastic response analysis and optimization of diverse nonlinear dynamic systems. [Internet] [Doctoral dissertation]. Columbia University; 2020. [cited 2021 Mar 06].
Available from: https://doi.org/10.7916/d8-6p2s-hr09.
Council of Science Editors:
Petromichelakis I. Path integral techniques and Gröbner basis approaches for stochastic response analysis and optimization of diverse nonlinear dynamic systems. [Doctoral Dissertation]. Columbia University; 2020. Available from: https://doi.org/10.7916/d8-6p2s-hr09
Columbia University
19.
He, Fei.
Distributionally Robust Performance Analysis: Data, Dependence and Extremes.
Degree: 2018, Columbia University
URL: https://doi.org/10.7916/D8MP6M41
► This dissertation focuses on distributionally robust performance analysis, which is an area of applied probability whose aim is to quantify the impact of model errors.…
(more)
▼ This dissertation focuses on distributionally robust performance analysis, which is an area of applied probability whose aim is to quantify the impact of model errors. Stochastic models are built to describe phenomena of interest with the intent of gaining insights or making informed decisions. Typically, however, the fidelity of these models (i.e. how closely they describe the underlying reality) may be compromised due to either the lack of information available or tractability considerations. The goal of distributionally robust performance analysis is then to quantify, and potentially mitigate, the impact of errors or model misspecifications. As such, distributionally robust performance analysis affects virtually any area in which stochastic modelling is used for analysis or decision making.
This dissertation studies various aspects of distributionally robust performance analysis. For example, we are concerned with quantifying the impact of model error in tail estimation using extreme value theory. We are also concerned with the impact of the dependence structure in risk analysis when marginal distributions of risk factors are known. In addition, we also are interested in connections recently found to machine learning and other statistical estimators which are based on distributionally robust optimization.
The first problem that we consider consists in studying the impact of model specification in the context of extreme quantiles and tail probabilities. There is a rich statistical theory that allows to extrapolate tail behavior based on limited information. This body of theory is known as extreme value theory and it has been successfully applied to a wide range of settings, including building physical infrastructure to withstand extreme environmental events and also guiding the capital requirements of insurance companies to ensure their financial solvency. Not surprisingly, attempting to extrapolate out into the tail of a distribution from limited observations requires imposing assumptions which are impossible to verify. The assumptions imposed in extreme value theory imply that a parametric family of models (known as generalized extreme value distributions) can be used to perform tail estimation. Because such assumptions are so difficult (or impossible) to be verified, we use distributionally robust optimization to enhance extreme value statistical analysis. Our approach results in a procedure which can be easily applied in conjunction with standard extreme value analysis and we show that our estimators enjoy correct coverage even in settings in which the assumptions imposed by extreme value theory fail to hold.
In addition to extreme value estimation, which is associated to risk analysis via extreme events, another feature which often plays a role in the risk analysis is the impact of dependence structure among risk factors. In the second chapter we study the question of evaluating the worst-case expected cost involving two sources of uncertainty, each of them with a specific marginal…
Subjects/Keywords: Operations research; Performance – Analysis; Stochastic models; Probabilities
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APA (6th Edition):
He, F. (2018). Distributionally Robust Performance Analysis: Data, Dependence and Extremes. (Doctoral Dissertation). Columbia University. Retrieved from https://doi.org/10.7916/D8MP6M41
Chicago Manual of Style (16th Edition):
He, Fei. “Distributionally Robust Performance Analysis: Data, Dependence and Extremes.” 2018. Doctoral Dissertation, Columbia University. Accessed March 06, 2021.
https://doi.org/10.7916/D8MP6M41.
MLA Handbook (7th Edition):
He, Fei. “Distributionally Robust Performance Analysis: Data, Dependence and Extremes.” 2018. Web. 06 Mar 2021.
Vancouver:
He F. Distributionally Robust Performance Analysis: Data, Dependence and Extremes. [Internet] [Doctoral dissertation]. Columbia University; 2018. [cited 2021 Mar 06].
Available from: https://doi.org/10.7916/D8MP6M41.
Council of Science Editors:
He F. Distributionally Robust Performance Analysis: Data, Dependence and Extremes. [Doctoral Dissertation]. Columbia University; 2018. Available from: https://doi.org/10.7916/D8MP6M41
University of Oxford
20.
Kolliopoulos, Nikolaos.
Analysis of stochastic PDEs arising from large portfolios of stochastic volatility models.
Degree: PhD, 2018, University of Oxford
URL: http://ora.ox.ac.uk/objects/uuid:1373d822-adcf-4406-80e7-3eb70900eb9f
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.770713
► The aim of this thesis is to study a large market model of defaultable assets in which the asset price processes are modelled as stochastic…
(more)
▼ The aim of this thesis is to study a large market model of defaultable assets in which the asset price processes are modelled as stochastic volatility models with volatility mean-reversion and default upon hitting a lower boundary. We assume that both the asset prices and their volatilities are correlated through systemic Brownian motions. In the first part of the thesis, we are interested in the loss process that arises in this setting and we prove the existence of a large portfolio limit for the empirical measure process of this system. This limit evolves as a measure valued process and we show that it will have a density given in terms of a solution to a stochastic partial differential equation of filtering type in the two-dimensional half-space, with a Dirichlet boundary condition. Next, we employ Malliavin calculus to establish the existence of a regular density for the volatility component of the SPDE, and an approximation by models of piecewise constant volatilities combined with a kernel smoothing technique to obtain existence and regularity for the full two-dimensional filtering problem. We are able to establish good regularity properties and uniqueness for solutions, except in the CIR case where uniqueness remains an open problem. In the second part of the thesis, we study the convergence of the total mass of a solution to this stochastic initial-boundary value problem when the mean-reversion coefficients of the volatilities are multiples of a parameter which tends to infinity. When the coefficients of the noises of the volatilities are multiples of the square root of the same parameter, the convergence is extremely weak. On the other hand, when the noise coefficients are independent of this exploding parameter, the volatilities converge to their means and we can have much better approximations. Such approximations can be used to improve the accuracy of certain risk-management methods in markets where fast volatility mean-reversion is observed.
Subjects/Keywords: 519; Risk management; Mathematical Finance; Stochastic analysis
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APA (6th Edition):
Kolliopoulos, N. (2018). Analysis of stochastic PDEs arising from large portfolios of stochastic volatility models. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:1373d822-adcf-4406-80e7-3eb70900eb9f ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.770713
Chicago Manual of Style (16th Edition):
Kolliopoulos, Nikolaos. “Analysis of stochastic PDEs arising from large portfolios of stochastic volatility models.” 2018. Doctoral Dissertation, University of Oxford. Accessed March 06, 2021.
http://ora.ox.ac.uk/objects/uuid:1373d822-adcf-4406-80e7-3eb70900eb9f ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.770713.
MLA Handbook (7th Edition):
Kolliopoulos, Nikolaos. “Analysis of stochastic PDEs arising from large portfolios of stochastic volatility models.” 2018. Web. 06 Mar 2021.
Vancouver:
Kolliopoulos N. Analysis of stochastic PDEs arising from large portfolios of stochastic volatility models. [Internet] [Doctoral dissertation]. University of Oxford; 2018. [cited 2021 Mar 06].
Available from: http://ora.ox.ac.uk/objects/uuid:1373d822-adcf-4406-80e7-3eb70900eb9f ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.770713.
Council of Science Editors:
Kolliopoulos N. Analysis of stochastic PDEs arising from large portfolios of stochastic volatility models. [Doctoral Dissertation]. University of Oxford; 2018. Available from: http://ora.ox.ac.uk/objects/uuid:1373d822-adcf-4406-80e7-3eb70900eb9f ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.770713
21.
Valentin, Jérôme.
Extensions de la formule d'Itô par le calcul de Malliavin et application à un problème variationnel : Extensions of the Itô formula through Malliavin calculus and application to a variational problem.
Degree: Docteur es, Informatique et réseaux, 2012, Paris, ENST
URL: http://www.theses.fr/2012ENST0029
► Ce travail de thèse est consacré à l'extension de la formule d'Itô au cas de chemins à variations bornées à valeurs dans l'espace des distributions…
(more)
▼ Ce travail de thèse est consacré à l'extension de la formule d'Itô au cas de chemins à variations bornées à valeurs dans l'espace des distributions tempérées composés par des processus réguliers au sens de Malliavin. On s'attache en particulier à faire des hypothèses de régularité minimales, ce qui donne accès à un certain nombre d'applications de notre principal résultat, en particulier à l'étude d'un problème variationnel. Le premier chapitre est consacré à des rappels de calcul de Malliavin. Le deuxième donne des résultats sur la topologie sur la classe de Schwartz et l'espace des distributions tempérées. Dans le troisième chapitre, on donne des conditions optimales sous lesquelles on peut définir la composition d'une distribution tempérée par une variable aléatoire et quelle est la régularité au sens de Malliavin de l'objet ainsi construit. Des techniques d'interpolation permettent d'obtenir des résultats pour des espaces fractionnaires. On donne également des résultats pour le cas où la distribution est elle-même stochastique. Ces résultats nous permettent d'écrire, au chapitre 4, une formule d'Ito faible s'appliquant sous des hypothèses beaucoup plus faibles que celles généralement proposées dans la littérature. On donne aussi une version anticipative et une formule de type Ito-Wentzell. On donne des résultats plus précis dans le cas où le processus auquel on applique notre formule est la solution d'une EDS simple et on applique ce résultat à l'étude de la régularité du temps local en dimension quelconque. Enfin le cinquième chapitre résout un problème variationnel simple en affaiblissant considérablement une hypothèse d'ellipticité faite par la plupart des auteurs.
This dissertation studies the extension of the Itô formula to the case of distibution-valued paths of bounded variation lifted by processes which are regular in the sense of Malliavin calculus. We make optimal hypotheses, which gives us access to many applications. The first chapter is a primer in Malliavin calculus. The second chapter provides useful results on the toplogy of the schwartz class and of the space of tempered distributions. in the third chapter, we give optimal conditions under which a tempered distribution may be composed by a random variable and we study the malliavin regularity of the object thus defined. Interpolation techniques give access to results in fractional spaces. We also give results for the case where the tempered distribution is itself stochastic. These results allow us to obtain, in chapter 4, a weak Itô formula under hypotheses which are much weaker than those usually made in the litterature. We also give an Itô-Wentzell and an anticipative version. In the case where the process to which the ito formula is applied is the solution to an SDE, we give a more precise result, which we use to study the reguarity of the multi-dimensional local time. Finally the fifth chapter solves a variational problem under hypotheses which are much weaker than the usual assumption of hypoellipticity
Advisors/Committee Members: Ustunel, Ali Suleyman (thesis director).
Subjects/Keywords: Analyse stochastique; Hypoellipticité; Stochastic analysis; Hypoellipticity
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APA (6th Edition):
Valentin, J. (2012). Extensions de la formule d'Itô par le calcul de Malliavin et application à un problème variationnel : Extensions of the Itô formula through Malliavin calculus and application to a variational problem. (Doctoral Dissertation). Paris, ENST. Retrieved from http://www.theses.fr/2012ENST0029
Chicago Manual of Style (16th Edition):
Valentin, Jérôme. “Extensions de la formule d'Itô par le calcul de Malliavin et application à un problème variationnel : Extensions of the Itô formula through Malliavin calculus and application to a variational problem.” 2012. Doctoral Dissertation, Paris, ENST. Accessed March 06, 2021.
http://www.theses.fr/2012ENST0029.
MLA Handbook (7th Edition):
Valentin, Jérôme. “Extensions de la formule d'Itô par le calcul de Malliavin et application à un problème variationnel : Extensions of the Itô formula through Malliavin calculus and application to a variational problem.” 2012. Web. 06 Mar 2021.
Vancouver:
Valentin J. Extensions de la formule d'Itô par le calcul de Malliavin et application à un problème variationnel : Extensions of the Itô formula through Malliavin calculus and application to a variational problem. [Internet] [Doctoral dissertation]. Paris, ENST; 2012. [cited 2021 Mar 06].
Available from: http://www.theses.fr/2012ENST0029.
Council of Science Editors:
Valentin J. Extensions de la formule d'Itô par le calcul de Malliavin et application à un problème variationnel : Extensions of the Itô formula through Malliavin calculus and application to a variational problem. [Doctoral Dissertation]. Paris, ENST; 2012. Available from: http://www.theses.fr/2012ENST0029
Michigan State University
22.
Liu, Ming-Shou.
Development and analysis of an optimal bounding ellipsoid algorithm using stochastic approximation.
Degree: PhD, Department of Electrical Engineering, 1993, Michigan State University
URL: http://etd.lib.msu.edu/islandora/object/etd:22532
Subjects/Keywords: Algorithms; Stochastic analysis
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APA (6th Edition):
Liu, M. (1993). Development and analysis of an optimal bounding ellipsoid algorithm using stochastic approximation. (Doctoral Dissertation). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:22532
Chicago Manual of Style (16th Edition):
Liu, Ming-Shou. “Development and analysis of an optimal bounding ellipsoid algorithm using stochastic approximation.” 1993. Doctoral Dissertation, Michigan State University. Accessed March 06, 2021.
http://etd.lib.msu.edu/islandora/object/etd:22532.
MLA Handbook (7th Edition):
Liu, Ming-Shou. “Development and analysis of an optimal bounding ellipsoid algorithm using stochastic approximation.” 1993. Web. 06 Mar 2021.
Vancouver:
Liu M. Development and analysis of an optimal bounding ellipsoid algorithm using stochastic approximation. [Internet] [Doctoral dissertation]. Michigan State University; 1993. [cited 2021 Mar 06].
Available from: http://etd.lib.msu.edu/islandora/object/etd:22532.
Council of Science Editors:
Liu M. Development and analysis of an optimal bounding ellipsoid algorithm using stochastic approximation. [Doctoral Dissertation]. Michigan State University; 1993. Available from: http://etd.lib.msu.edu/islandora/object/etd:22532
Colorado School of Mines
23.
Williams, John.
Building a better wind forecast: a stochastic forecast system using a fully-coupled hydrologic-atmospheric model.
Degree: PhD, Geology and Geological Engineering, 2012, Colorado School of Mines
URL: http://hdl.handle.net/11124/76832
► Wind power is rapidly gaining prominence as a major source of renewable energy. Harnessing this promising energy source is challenging because of the intermittent nature…
(more)
▼ Wind power is rapidly gaining prominence as a major source of renewable energy. Harnessing this promising energy source is challenging because of the intermittent nature of wind and its propensity to change speed and direction over short time scales. Accurate forecasting tools are critical to support the integration of wind energy into power grids and to maximize its impact on renewable energy portfolios. A numerical weather prediction tool is limited by model errors arising from simplifications in the way it represents the physics of the natural system. Land surface - atmosphere feedbacks are strongly dependent on both atmospheric processes and hydrologic processes at and below the land surface. It has been shown in the literature that improving the physical representation of these feedbacks leads to better forecast results for precipitation distribution and wind speeds. Key to this physical representation is soil moisture distribution. By using PF.WRF, a fully-coupled hydrologic and atmospheric model incorporating the ParFlow hydrologic model in the the Weather Research and Forecasting atmospheric code, it is possible to dynamically simulate water movements in the subsurface generating more realistic soil moisture fields to interact directly with atmospheric processes. This work traces uncertainty propagation from subsurface hydraulic conductivity through soil moisture and latent heat flux and into the atmosphere to analyze its impact on wind speed, the extent of that impact in the presence of prevailing winds, and the length scales over which that impact is important. A data assimilation system using an implementation of the ensemble Kalman filter is developed and verified to reduce uncertainty in simulated wind speed by informing the forecast system with observed soil moisture values, demonstrating that even in a small model domain wind speed is sensitive to variation in soil moisture distribution.
Advisors/Committee Members: Maxwell, Reed M. (advisor), Cohen, Ronald R. H. (committee member), Delle Monache, Luca (committee member), Hering, Amanda S. (committee member), Lundquist, Julie K. (committee member).
Subjects/Keywords: Wind forecasting; Wind power – Forecasting; Stochastic analysis
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APA (6th Edition):
Williams, J. (2012). Building a better wind forecast: a stochastic forecast system using a fully-coupled hydrologic-atmospheric model. (Doctoral Dissertation). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/76832
Chicago Manual of Style (16th Edition):
Williams, John. “Building a better wind forecast: a stochastic forecast system using a fully-coupled hydrologic-atmospheric model.” 2012. Doctoral Dissertation, Colorado School of Mines. Accessed March 06, 2021.
http://hdl.handle.net/11124/76832.
MLA Handbook (7th Edition):
Williams, John. “Building a better wind forecast: a stochastic forecast system using a fully-coupled hydrologic-atmospheric model.” 2012. Web. 06 Mar 2021.
Vancouver:
Williams J. Building a better wind forecast: a stochastic forecast system using a fully-coupled hydrologic-atmospheric model. [Internet] [Doctoral dissertation]. Colorado School of Mines; 2012. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/11124/76832.
Council of Science Editors:
Williams J. Building a better wind forecast: a stochastic forecast system using a fully-coupled hydrologic-atmospheric model. [Doctoral Dissertation]. Colorado School of Mines; 2012. Available from: http://hdl.handle.net/11124/76832
Macquarie University
24.
Gretz, Friedrich.
Semantics and loop invariant synthesis for probabilistic programs.
Degree: 2015, Macquarie University
URL: http://hdl.handle.net/1959.14/1051765
► "A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy in the Department of Computing, Faculty of Science and Engineering,…
(more)
▼ "A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy in the Department of Computing, Faculty of Science and Engineering, Macquarie University".
"2014".
Bibliography: pages 75-82.
1. Introduction – 2. Linking operational and denotational semantics – 3. Conditional probabilities and expectations – 4. Automated analysis – Chapter 5. Conclusion and future work – Appendices.
In this thesis we consider sequential probabilistic programs. Such programs are a means to model randomised algorithms in computer science. They facilitate the formal analysis of performance and correctness of algorithms or security aspects of protocols. We develop an operational semantics for probabilistic programs and show it to be equivalent to the expectation transformer semantics due to McIver and Morgan. This connection between the two kinds of semantics provides a deeper understanding of the behaviour of probabilistic programs and is instrumental to transfer results between communities that use transition systems such as Markov decision processes to reason about probabilistic behaviour and communities that focus on deductive verification techniques based on expectation transformers. As a next step, we add the concept of observations and extend both semantics to facilitate the calculation of expectations which are conditioned on the fact that no observation is violated during the program's execution. Our main contribution here is to explore issues that arise with non-terminating, non-deterministic or infeasible programs and provide semantics that are generally applicable. Additionally, we discuss several program transformation to facilitate the understanding of conditioning in probabilistic programming. In the last part of the thesis we turn our attention to the automated verification of probabilistic programs. We are interested in automating inductive verification techniques. As usual the main obstacle in program analysis are loops which require either the calculation of fixed points or the generation of inductive invariants for their analysis. This task, which is already hard for standard, i.e. non-probabilistic, programs, becomes even more challenging as our reasoning becomes quantitative. We focus on a technique to generate quantitative loop invariants from user defined templates. This approach is implemented in a software tool called Prinsys and evaluated on several examples.
1 online resource (x, 85 pages) illustrations (some coloured)
Advisors/Committee Members: Macquarie University. Department of Computing.
Subjects/Keywords: Probabilities – Computer simulation; Stochastic analysis; Computer algorithms
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APA (6th Edition):
Gretz, F. (2015). Semantics and loop invariant synthesis for probabilistic programs. (Doctoral Dissertation). Macquarie University. Retrieved from http://hdl.handle.net/1959.14/1051765
Chicago Manual of Style (16th Edition):
Gretz, Friedrich. “Semantics and loop invariant synthesis for probabilistic programs.” 2015. Doctoral Dissertation, Macquarie University. Accessed March 06, 2021.
http://hdl.handle.net/1959.14/1051765.
MLA Handbook (7th Edition):
Gretz, Friedrich. “Semantics and loop invariant synthesis for probabilistic programs.” 2015. Web. 06 Mar 2021.
Vancouver:
Gretz F. Semantics and loop invariant synthesis for probabilistic programs. [Internet] [Doctoral dissertation]. Macquarie University; 2015. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/1959.14/1051765.
Council of Science Editors:
Gretz F. Semantics and loop invariant synthesis for probabilistic programs. [Doctoral Dissertation]. Macquarie University; 2015. Available from: http://hdl.handle.net/1959.14/1051765
University of Georgia
25.
Chumbler, James Milton.
Utilization of logging capacity in the southern United States and Maine.
Degree: 2014, University of Georgia
URL: http://hdl.handle.net/10724/29390
► Timber harvesting businesses do not have a standard method to quantify performance or determine the capacity of an individual logging crew. Both productivity and efficiency…
(more)
▼ Timber harvesting businesses do not have a standard method to quantify performance or determine the capacity of an individual logging crew. Both productivity and efficiency are often used as measures of performance. Productivity is the ratio
of output to input. Efficiency is a comparison or ratio between an observed level of output and a benchmark, defined as the optimal level of output (capacity) for a given a level of input. This study attempts to define input, output, and a benchmarking
technique to estimate utilization of production capacity for individual logging crews. Approximately 60 logging crews provided weekly production data during 2000 and 2001. The weekly data serves as a quantitative narrative of the workweek, explaining the
number and types of loads hauled, the amount of labor employed, the number of moves, and the extent of use of contract trucking. To estimate technical efficiency, stochastic frontier analysis (SFA) was applied. A production frontier was estimated based
on production, labor, and capital expense estimate. The capital expense estimate uses each crew’s scheduled machine-hours and equipment mix to predict a cost per scheduled machine-hour. Explanatory environmental variables were tested for significance and
influence on production. SFA shows great promise as a means to benchmark logging crew production capacity.
Subjects/Keywords: Logging Efficiency; Logging Capacity; Stochastic Frontier Analysis
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APA (6th Edition):
Chumbler, J. M. (2014). Utilization of logging capacity in the southern United States and Maine. (Thesis). University of Georgia. Retrieved from http://hdl.handle.net/10724/29390
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Chumbler, James Milton. “Utilization of logging capacity in the southern United States and Maine.” 2014. Thesis, University of Georgia. Accessed March 06, 2021.
http://hdl.handle.net/10724/29390.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Chumbler, James Milton. “Utilization of logging capacity in the southern United States and Maine.” 2014. Web. 06 Mar 2021.
Vancouver:
Chumbler JM. Utilization of logging capacity in the southern United States and Maine. [Internet] [Thesis]. University of Georgia; 2014. [cited 2021 Mar 06].
Available from: http://hdl.handle.net/10724/29390.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Chumbler JM. Utilization of logging capacity in the southern United States and Maine. [Thesis]. University of Georgia; 2014. Available from: http://hdl.handle.net/10724/29390
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of New South Wales
26.
Schofield, Stuart Guy.
Corporate governance and the relevance of private equity.
Degree: Banking & Finance, 2014, University of New South Wales
URL: http://handle.unsw.edu.au/1959.4/53410
;
https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12105/SOURCE02?view=true
► In this thesis I examine the impact of private equity on improving the quality of corporate governance. Using stochastic frontier analysis I create a direct…
(more)
▼ In this thesis I examine the impact of private equity on improving the quality of corporate governance. Using
stochastic frontier
analysis I create a direct estimate of governance effectiveness having controlled for company and industry characteristics and also for chance events over time (following Habib et al. 1997). Using data from the U.S. for 2002-2006 I find that the average company’s value is 15 percent lower than that of a value maximising company. I then investigate the association between the shortfall and governance measures, employing both governance variables and governance factors that represent different dimensions of corporate governance. I find that governance can account for much of the shortfall in company value. The significance of incentive and monitoring mechanisms however varies according to the moral hazard environment. Given the mixed results in the literature on governance and performance, I corroborate and expand my findings by examining companies who were targets of private equity firms during the private equity wave of 2003-2007. Private equity practitioners see their contribution as “governance arbitrage”. I find evidence that supports this assertion. The data also suggest that the average company reduces its shortfall at a faster pace when there is a higher likelihood of a bid from a private equity firm. The relevance of private equity to the corporate governance process is therefore both direct (i.e., from a buyout and, in many cases, a later relisting) and indirect. These results cast new perspectives on the proposition that the public corporation has been “eclipsed” (Jensen 1989). Our results reveal that private equity does not so much threaten to eclipse the public corporation as act as a complementary external corporate governance mechanism to prevent the public corporation, in the longer term, from being eclipsed. I conclude that capital market participants such as private equity are therefore relevant to ensuring the survival of the public corporation by providing an additional mechanism to instigate change in a company’s governance.
Advisors/Committee Members: Adam, Chris, Banking & Finance, Australian School of Business, UNSW.
Subjects/Keywords: Stochastic Frontier Analysis; Corporate Governance; Private Equity
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APA (6th Edition):
Schofield, S. G. (2014). Corporate governance and the relevance of private equity. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/53410 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12105/SOURCE02?view=true
Chicago Manual of Style (16th Edition):
Schofield, Stuart Guy. “Corporate governance and the relevance of private equity.” 2014. Doctoral Dissertation, University of New South Wales. Accessed March 06, 2021.
http://handle.unsw.edu.au/1959.4/53410 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12105/SOURCE02?view=true.
MLA Handbook (7th Edition):
Schofield, Stuart Guy. “Corporate governance and the relevance of private equity.” 2014. Web. 06 Mar 2021.
Vancouver:
Schofield SG. Corporate governance and the relevance of private equity. [Internet] [Doctoral dissertation]. University of New South Wales; 2014. [cited 2021 Mar 06].
Available from: http://handle.unsw.edu.au/1959.4/53410 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12105/SOURCE02?view=true.
Council of Science Editors:
Schofield SG. Corporate governance and the relevance of private equity. [Doctoral Dissertation]. University of New South Wales; 2014. Available from: http://handle.unsw.edu.au/1959.4/53410 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12105/SOURCE02?view=true
University of New South Wales
27.
Pei, Yang.
An investigation of methodologies for stochastic simulation of helicopter accidents under autorotation scenarios.
Degree: Mechanical & Manufacturing Engineering, 2016, University of New South Wales
URL: http://handle.unsw.edu.au/1959.4/56911
;
https://unsworks.unsw.edu.au/fapi/datastream/unsworks:42023/SOURCE02?view=true
► Traditionally investigation into helicopter accidents has focused heavily on building complex, deterministic FE models and attempting to validate them with a small number of full…
(more)
▼ Traditionally investigation into helicopter accidents has focused heavily on building complex, deterministic FE models and attempting to validate them with a small number of full size crash tests. One of the major drawbacks of this methodology is that it does not address the dissimilarity of loads generated in nominally identical crashes. To take into account inherent uncertainties in the helicopter crashes, the classic deterministic approach has been replaced in this work by simulation using
stochastic algorithms. The chaotic nature, due to complexity in helicopter accidents, requires a much more robust simulation framework to capture a broad spectrum of potential crash scenarios.The thesis aims to investigate helicopter accidents resulting from engine failure by using
stochastic simulation methods. An innovative, hierarchical block structure for a
stochastic simulation is developed for investigating the variability in a full crash event reduced to two phases: flight emergency simulation and structure crash simulation. Non-parametric
analysis is performed on the
stochastic injury responses which attempt to predict the severity of the occupant’s injuries caused by helicopter accidents. The modelling framework establishes correlations between the critical parameters prior to helicopter accidents and possible occupant injury metrics. To achieve this aim, various
stochastic algorithms are performed throughout the
stochastic framework for the typical helicopter accidents. An investigation into helicopter accidents after engine failure is investigated by simulating auto-rotational flight within a range of sampled pre-event flight conditions to establish the correlation between initial flight parameters and the impact response. The structural crash simulation uses impact loads randomly selected from within the boundary of the flight simulation results to determine accelerations at the seat position. The potential injury is predicted by the stochastically generated acceleration peak-values the human body is subjected to and is evaluated by the resulting robust solution based on a computational geometry algorithm.A highly flexible, hierarchical,
stochastic simulation framework has been established for investigating helicopter accidents. It has been demonstrated for the case of complete engine failure during flight leading to autorotation. The significance of this approach is the resulting combination of a complete crash event into a single framework which can be robustly analysed to study the limits of occupant harm. This work will lead to strategies for minimizing occupant harm and maximizing survivability for a wide range of helicopter accident scenarios by both structural modification and flight procedural changes. Some techniques supporting the
stochastic analysis are successfully used offering the possibility of projecting the methodology into other engineering domains.
Advisors/Committee Members: Page, John, Mechanical & Manufacturing Engineering, Faculty of Engineering, UNSW, Pearce, Garth, Mechanical & Manufacturing Engineering, Faculty of Engineering, UNSW.
Subjects/Keywords: Non-parametric analysis; Stochastic simulation; Helicopter accident
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APA (6th Edition):
Pei, Y. (2016). An investigation of methodologies for stochastic simulation of helicopter accidents under autorotation scenarios. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/56911 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:42023/SOURCE02?view=true
Chicago Manual of Style (16th Edition):
Pei, Yang. “An investigation of methodologies for stochastic simulation of helicopter accidents under autorotation scenarios.” 2016. Doctoral Dissertation, University of New South Wales. Accessed March 06, 2021.
http://handle.unsw.edu.au/1959.4/56911 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:42023/SOURCE02?view=true.
MLA Handbook (7th Edition):
Pei, Yang. “An investigation of methodologies for stochastic simulation of helicopter accidents under autorotation scenarios.” 2016. Web. 06 Mar 2021.
Vancouver:
Pei Y. An investigation of methodologies for stochastic simulation of helicopter accidents under autorotation scenarios. [Internet] [Doctoral dissertation]. University of New South Wales; 2016. [cited 2021 Mar 06].
Available from: http://handle.unsw.edu.au/1959.4/56911 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:42023/SOURCE02?view=true.
Council of Science Editors:
Pei Y. An investigation of methodologies for stochastic simulation of helicopter accidents under autorotation scenarios. [Doctoral Dissertation]. University of New South Wales; 2016. Available from: http://handle.unsw.edu.au/1959.4/56911 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:42023/SOURCE02?view=true
Michigan State University
28.
Mandour, Gihan.
The QOBE algorithm : stochastic convergence analysis and application to classification.
Degree: PhD, 2003, Michigan State University
URL: http://etd.lib.msu.edu/islandora/object/etd:32243
Subjects/Keywords: Algorithms; Stochastic analysis
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APA (6th Edition):
Mandour, G. (2003). The QOBE algorithm : stochastic convergence analysis and application to classification. (Doctoral Dissertation). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:32243
Chicago Manual of Style (16th Edition):
Mandour, Gihan. “The QOBE algorithm : stochastic convergence analysis and application to classification.” 2003. Doctoral Dissertation, Michigan State University. Accessed March 06, 2021.
http://etd.lib.msu.edu/islandora/object/etd:32243.
MLA Handbook (7th Edition):
Mandour, Gihan. “The QOBE algorithm : stochastic convergence analysis and application to classification.” 2003. Web. 06 Mar 2021.
Vancouver:
Mandour G. The QOBE algorithm : stochastic convergence analysis and application to classification. [Internet] [Doctoral dissertation]. Michigan State University; 2003. [cited 2021 Mar 06].
Available from: http://etd.lib.msu.edu/islandora/object/etd:32243.
Council of Science Editors:
Mandour G. The QOBE algorithm : stochastic convergence analysis and application to classification. [Doctoral Dissertation]. Michigan State University; 2003. Available from: http://etd.lib.msu.edu/islandora/object/etd:32243
University of Oxford
29.
Crewe, Paul.
Some problems in abstract stochastic differential equations on Banach spaces.
Degree: PhD, 2011, University of Oxford
URL: http://ora.ox.ac.uk/objects/uuid:195c374f-3181-41b9-92d7-b375701a0b81
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.580891
► This thesis studies abstract stochastic differential equations on Banach spaces. The well-posedness of abstract stochastic differential equations on such spaces is a recent result of…
(more)
▼ This thesis studies abstract stochastic differential equations on Banach spaces. The well-posedness of abstract stochastic differential equations on such spaces is a recent result of van Neerven, Veraar and Weis, based on the theory of stochastic integration of Banach space valued processes constructed by the same authors. We study existence and uniqueness for solutions of stochastic differential equations with (possibly infinite) delay in their inputs on UMD Banach spaces. Such problems are also known as functional differential equations or delay differential equations. We show that the methods of van Neerven et al. extend to such problems if the initial history of the system lies in a space of a type introduced by Hale and Kato. The results are essentially of a fixed point type, both autonomous and non-autonomous cases are discussed and an example is given. We also study some long time properties of solutions to these stochastic differential equations on general Banach spaces. We show the existence of solutions to stochastic problems with almost periodicity in a weak or distributional sense. Results are again given for both autonomous and non-autonomous cases and depend heavily on estimates for R-bounds of operator families developed by Veraar. An example is given for a second order differential operator on a domain in ℝd. Finally we consider the existence of invariant measures for such problems. This extends recent work of van Gaans in Hilbert spaces to Banach spaces of type 2.
Subjects/Keywords: 518; Functional analysis (mathematics); stochastic differential equations; stochastic integration; Banach space; functional analysis
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APA (6th Edition):
Crewe, P. (2011). Some problems in abstract stochastic differential equations on Banach spaces. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:195c374f-3181-41b9-92d7-b375701a0b81 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.580891
Chicago Manual of Style (16th Edition):
Crewe, Paul. “Some problems in abstract stochastic differential equations on Banach spaces.” 2011. Doctoral Dissertation, University of Oxford. Accessed March 06, 2021.
http://ora.ox.ac.uk/objects/uuid:195c374f-3181-41b9-92d7-b375701a0b81 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.580891.
MLA Handbook (7th Edition):
Crewe, Paul. “Some problems in abstract stochastic differential equations on Banach spaces.” 2011. Web. 06 Mar 2021.
Vancouver:
Crewe P. Some problems in abstract stochastic differential equations on Banach spaces. [Internet] [Doctoral dissertation]. University of Oxford; 2011. [cited 2021 Mar 06].
Available from: http://ora.ox.ac.uk/objects/uuid:195c374f-3181-41b9-92d7-b375701a0b81 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.580891.
Council of Science Editors:
Crewe P. Some problems in abstract stochastic differential equations on Banach spaces. [Doctoral Dissertation]. University of Oxford; 2011. Available from: http://ora.ox.ac.uk/objects/uuid:195c374f-3181-41b9-92d7-b375701a0b81 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.580891
University of New South Wales
30.
Kepple, Jendi.
Stochastic Methods for Robust Design of Launch Vehicle Structures.
Degree: Mechanical & Manufacturing Engineering, 2016, University of New South Wales
URL: http://handle.unsw.edu.au/1959.4/56626
;
https://unsworks.unsw.edu.au/fapi/datastream/unsworks:41061/SOURCE02?view=true
► The important role of initial imperfections on decreasing the buckling load of imperfection sensitive thin-shelled structures, commonly used on launch vehicles such as the Ariane…
(more)
▼ The important role of initial imperfections on decreasing the buckling load of imperfection sensitive thin-shelled structures, commonly used on launch vehicles such as the Ariane family, has been widely studied since the 1930s. Research in this area has resulted in a variety of analytical and empirical design procedures to account for the diminished buckling loads of such shells. Some notable design guidelines which were formulated in the 1960s and are currently being used are the NASA-SP 8007 for imperfection sensitive cylinders and the NASA-SP 8019 for truncated cones; both of which are based on the lower-bound curve of empirical data. The guidelines have since been determined to be conservative and therefore unsuitable for composite structures, as they were developed for shells constructed from isotropic materials. Numerical
stochastic methods may provide a cheap and rapid solution to the calculation of knock-down factors for composite shells through their ability to incorporate a wide range of complicated imperfection types intrinsic to composites. Currently, there is no method that is able to stochastically replicate the full range of realistic imperfections for a full account of possible buckling loads. A procedure which aims to improve the
stochastic modelling of thickness and material imperfections in imperfection sensitive composite cylindrical and conical shells is investigated in this thesis. Monte Carlo simulations of axially compressed cylinders and truncated cones are performed to show that the proposed
stochastic methods are able to capture the scatter in buckling loads introduced from the imperfections. When paired with other imperfection types, the simulations are able to replicate the range of buckling loads seen in test situations. The
stochastic approaches developed here are also used to compare and validate the accuracy of the knock-down factors calculated by a newly proposed method called the ‘Single Perturbation Load Approach’ (SPLA), for a variety of conical geometries and lay-ups. Comparison with experimental results of a truncated cone supports the assumptions used in the simulations.
Advisors/Committee Members: Pearce, Garth, Mechanical & Manufacturing Engineering, Faculty of Engineering, UNSW, Prusty, Gangadhara, Mechanical & Manufacturing Engineering, Faculty of Engineering, UNSW.
Subjects/Keywords: Spectral analysis; Buckling; Stochastic analysis; Thin-walled structures; Finite element analysis
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Kepple, J. (2016). Stochastic Methods for Robust Design of Launch Vehicle Structures. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/56626 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:41061/SOURCE02?view=true
Chicago Manual of Style (16th Edition):
Kepple, Jendi. “Stochastic Methods for Robust Design of Launch Vehicle Structures.” 2016. Doctoral Dissertation, University of New South Wales. Accessed March 06, 2021.
http://handle.unsw.edu.au/1959.4/56626 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:41061/SOURCE02?view=true.
MLA Handbook (7th Edition):
Kepple, Jendi. “Stochastic Methods for Robust Design of Launch Vehicle Structures.” 2016. Web. 06 Mar 2021.
Vancouver:
Kepple J. Stochastic Methods for Robust Design of Launch Vehicle Structures. [Internet] [Doctoral dissertation]. University of New South Wales; 2016. [cited 2021 Mar 06].
Available from: http://handle.unsw.edu.au/1959.4/56626 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:41061/SOURCE02?view=true.
Council of Science Editors:
Kepple J. Stochastic Methods for Robust Design of Launch Vehicle Structures. [Doctoral Dissertation]. University of New South Wales; 2016. Available from: http://handle.unsw.edu.au/1959.4/56626 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:41061/SOURCE02?view=true
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Open Access Theses and Dissertations
