subject:(Stochastic Differential Equations)

Columbia University

1. Ozen, Hasan Cagan. Long Time Propagation of Stochasticity by Dynamical Polynomial Chaos Expansions.

Degree: 2017, Columbia University

► Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) play an important role in many areas of engineering and applied sciences such as atmospheric… (more)

▼ Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) play an important role in many areas of engineering and applied sciences such as atmospheric sciences, mechanical and aerospace engineering, geosciences, and finance. Equilibrium statistics and long-time solutions of these equations are pertinent to many applications. Typically, these models contain several uncertain parameters which need to be propagated in order to facilitate uncertainty quantification and prediction. Correspondingly, in this thesis, we propose a generalization of the Polynomial Chaos (PC) framework for long-time solutions of SDEs and SPDEs driven by Brownian motion forcing. Polynomial chaos expansions (PCEs) allow us to propagate uncertainties in the coefficients of these equations to the statistics of their solutions. Their main advantages are: (i) they replace stochastic equations by systems of deterministic equations; and (ii) they provide fast convergence. Their main challenge is that the computational cost becomes prohibitive when the dimension of the parameters modeling the stochasticity is even moderately large. In particular, for equations with Brownian motion forcing, the long-time simulation by PC-based methods is notoriously difficult as the dimension of stochastic variables increases with time. With the goal in mind to deliver computationally efficient numerical algorithms for stochastic equations in the long time, our main strategy is to leverage the intrinsic sparsity in the dynamics by identifying the influential random parameters and construct spectral approximations to the solutions in terms of those relevant variables. Once this strategy is employed dynamically in time, using online constructions, approximations can retain their sparsity and accuracy; even for long times. To this end, exploiting Markov property of Brownian motion, we present a restart procedure that allows PCEs to expand the solutions at future times in terms of orthogonal polynomials of the measure describing the solution at a given time and the future Brownian motion. In case of SPDEs, the Karhunen-Loeve expansion (KLE) is applied at each restart to select the influential variables and keep the dimensionality minimal. Using frequent restarts and low degree polynomials, the algorithms are able to capture long-time solutions accurately. We will also introduce, using the same principles, a similar algorithm based on a stochastic collocation method for the solutions of SDEs. We apply the methods to the numerical simulation of linear and nonlinear SDEs, and stochastic Burgers and Navier-Stokes equations with white noise forcing. Our methods also allow us to incorporate time-independent random coefficients such as a random viscosity. We propose several numerical simulations, and show that the algorithms compare favorably with standard Monte Carlo methods in terms of accuracy and computational times. To demonstrate the efficiency of the algorithms for long-time simulations, we compute invariant measures of…

Subjects/Keywords: Mathematics; Stochastic differential equations; Algorithms

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APA (6^th Edition):

Ozen, H. C. (2017). Long Time Propagation of Stochasticity by Dynamical Polynomial Chaos Expansions. (Doctoral Dissertation). Columbia University. Retrieved from https://doi.org/10.7916/D8WH32C5

Chicago Manual of Style (16^th Edition):

Ozen, Hasan Cagan. “Long Time Propagation of Stochasticity by Dynamical Polynomial Chaos Expansions.” 2017. Doctoral Dissertation, Columbia University. Accessed June 16, 2019. https://doi.org/10.7916/D8WH32C5.

MLA Handbook (7^th Edition):

Ozen, Hasan Cagan. “Long Time Propagation of Stochasticity by Dynamical Polynomial Chaos Expansions.” 2017. Web. 16 Jun 2019.

Vancouver:

Ozen HC. Long Time Propagation of Stochasticity by Dynamical Polynomial Chaos Expansions. [Internet] [Doctoral dissertation]. Columbia University; 2017. [cited 2019 Jun 16]. Available from: https://doi.org/10.7916/D8WH32C5.

Council of Science Editors:

Ozen HC. Long Time Propagation of Stochasticity by Dynamical Polynomial Chaos Expansions. [Doctoral Dissertation]. Columbia University; 2017. Available from: https://doi.org/10.7916/D8WH32C5

University of Kansas

2. Lewis, Peter. Regularity of Stochastic Burgers’-Type Equations.

Degree: PhD, Mathematics, 2018, University of Kansas

URL: http://hdl.handle.net/1808/27802

► In classical partial differential equations (PDEs), it is well known that the solution to Burgers' equation in one spatial dimension with positive viscosity can be… (more)

▼ In classical partial differential equations (PDEs), it is well known that the solution to Burgers' equation in one spatial dimension with positive viscosity can be solved by the so called Hopf-Cole transformation, which linearizes the PDE. In particular, this converts Burgers' equation to the linear heat equation, which can be solved explicitly. On the other hand, the Feynman-Kac formula is a tool that can be used to solve the heat equation probabilistically. An interesting and perhaps surprising result which we prove is that one can still make sense of these approaches to Burgers' equation in the presence of space-time white noise, which is very rough. After proving that a suitable Feynman-Kac representation solves stochastic Burgers' equation under a Hopf-Cole transformation, we study some regularity properties of this solution. In particular, we prove moment estimates and Holder continuity, which can be thought of as how ``big'' the solution gets in time and space, and how ``rough'' this solution can be. From this, we then obtain sub-exponential moments and bounds on the tails of the probability distribution for the solution. Prior to this work, no results about any kinds of moment estimates or tails of distributions for stochastic Burgers'-type equations had been established. Furthermore, only one publication on Burgers' equation contains a discussion of Holder regularity. Given the solution to a stochastic partial differential equation (SPDE), it is natural to ask whether this stochastic process has a well-behaved probability law. For example, does the solution have a smooth probability density function or just an absolutely continuous one? Using some powerful tools from Malliavin calculus, we answer this question for stochastic Burgers' equation with our Hopf-Cole solution. Finally, we study regularity of the probability law of the solution to a more general class of semilinear SPDEs which contain Burgers' equation as an example. These results take a less tangible approach since there is no explicit representation for solutions to these equations. However, as we will see, there are some clever techniques and interesting results that can be used to establish such properties. For example, we prove a comparison theorem for this class of SPDEs which, interestingly enough, will be instrumental in obtaining regularity of the probability density function of the solution at fixed points in time and space. The projects in this thesis are joint work of the author and David Nualart. Advisors/Committee Members: Nualart, David (advisor), Alexander, Perry (cmtemember), Feng, Jin (cmtemember), Johnson, Mat (cmtemember), Soo, Terry (cmtemember).

Subjects/Keywords: Mathematics; Stochastic partial differential equations

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APA (6^th Edition):

Lewis, P. (2018). Regularity of Stochastic Burgers’-Type Equations. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/27802

Chicago Manual of Style (16^th Edition):

Lewis, Peter. “Regularity of Stochastic Burgers’-Type Equations.” 2018. Doctoral Dissertation, University of Kansas. Accessed June 16, 2019. http://hdl.handle.net/1808/27802.

MLA Handbook (7^th Edition):

Lewis, Peter. “Regularity of Stochastic Burgers’-Type Equations.” 2018. Web. 16 Jun 2019.

Vancouver:

Lewis P. Regularity of Stochastic Burgers’-Type Equations. [Internet] [Doctoral dissertation]. University of Kansas; 2018. [cited 2019 Jun 16]. Available from: http://hdl.handle.net/1808/27802.

Council of Science Editors:

Lewis P. Regularity of Stochastic Burgers’-Type Equations. [Doctoral Dissertation]. University of Kansas; 2018. Available from: http://hdl.handle.net/1808/27802

University of Pretoria

3. Ali, Zakaria Idriss. Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth.

Degree: Mathematics and Applied Mathematics, 2011, University of Pretoria

URL: http://hdl.handle.net/2263/29519

► In this dissertation, we investigate a very interesting class of quasi-linear stochastic partial differential equations. The main purpose of this article is to prove an… (more)

Subjects/Keywords: Stochastic differential equations; Quasi-linear stochastic; UCTD

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APA (6^th Edition):

Ali, Z. I. (2011). Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth. (Masters Thesis). University of Pretoria. Retrieved from http://hdl.handle.net/2263/29519

Chicago Manual of Style (16^th Edition):

Ali, Zakaria Idriss. “Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth.” 2011. Masters Thesis, University of Pretoria. Accessed June 16, 2019. http://hdl.handle.net/2263/29519.

MLA Handbook (7^th Edition):

Ali, Zakaria Idriss. “Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth.” 2011. Web. 16 Jun 2019.

Vancouver:

Ali ZI. Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth. [Internet] [Masters thesis]. University of Pretoria; 2011. [cited 2019 Jun 16]. Available from: http://hdl.handle.net/2263/29519.

Council of Science Editors:

Ali ZI. Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth. [Masters Thesis]. University of Pretoria; 2011. Available from: http://hdl.handle.net/2263/29519

University of Pretoria

4. [No author]. Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth .

Degree: 2011, University of Pretoria

URL: http://upetd.up.ac.za/thesis/available/etd-11172011-103734/

► In this dissertation, we investigate a very interesting class of quasi-linear stochastic partial differential equations. The main purpose of this article is to prove an… (more)

Subjects/Keywords: Stochastic differential equations; Quasi-linear stochastic; UCTD

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APA (6^th Edition):

author], [. (2011). Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth . (Masters Thesis). University of Pretoria. Retrieved from http://upetd.up.ac.za/thesis/available/etd-11172011-103734/

Chicago Manual of Style (16^th Edition):

author], [No. “Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth .” 2011. Masters Thesis, University of Pretoria. Accessed June 16, 2019. http://upetd.up.ac.za/thesis/available/etd-11172011-103734/.

MLA Handbook (7^th Edition):

author], [No. “Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth .” 2011. Web. 16 Jun 2019.

Vancouver:

author] [. Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth . [Internet] [Masters thesis]. University of Pretoria; 2011. [cited 2019 Jun 16]. Available from: http://upetd.up.ac.za/thesis/available/etd-11172011-103734/.

Council of Science Editors:

author] [. Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth . [Masters Thesis]. University of Pretoria; 2011. Available from: http://upetd.up.ac.za/thesis/available/etd-11172011-103734/

Loughborough University

5. Yeadon, Cyrus. Approximating solutions of backward doubly stochastic differential equations with measurable coefficients using a time discretization scheme.

Degree: PhD, 2015, Loughborough University

URL: https://dspace.lboro.ac.uk/2134/20643 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.682529

► It has been shown that backward doubly stochastic differential equations (BDSDEs) provide a probabilistic representation for a certain class of nonlinear parabolic stochastic partial differential… (more)

▼ It has been shown that backward doubly stochastic differential equations (BDSDEs) provide a probabilistic representation for a certain class of nonlinear parabolic stochastic partial differential equations (SPDEs). It has also been shown that the solution of a BDSDE with Lipschitz coefficients can be approximated by first discretizing time and then calculating a sequence of conditional expectations. Given fixed points in time and space, this approximation has been shown to converge in mean square. In this thesis, we investigate the approximation of solutions of BDSDEs with coefficients that are measurable in time and space using a time discretization scheme with a view towards applications to SPDEs. To achieve this, we require the underlying forward diffusion to have smooth coefficients and we consider convergence in a norm which includes a weighted spatial integral. This combination of smoother forward coefficients and weaker norm allows the use of an equivalence of norms result which is key to our approach. We additionally take a brief look at the approximation of solutions of a class of infinite horizon BDSDEs with a view towards approximating stationary solutions of SPDEs. Whilst we remain agnostic with regards to the implementation of our discretization scheme, our scheme should be amenable to a Monte Carlo simulation based approach. If this is the case, we propose that in addition to being attractive from a performance perspective in higher dimensions, such an approach has a potential advantage when considering measurable coefficients. Specifically, since we only discretize time and effectively rely on simulations of the underlying forward diffusion to explore space, we are potentially less vulnerable to systematically overestimating or underestimating the effects of coefficients with spatial discontinuities than alternative approaches such as finite difference or finite element schemes that do discretize space. Another advantage of the BDSDE approach is that it is possible to derive an upper bound on the error of our method for a fairly broad class of conditions in a single analysis. Furthermore, our conditions seem more general in some respects than is typically considered in the SPDE literature.

Subjects/Keywords: 519.2; Backward doubly stochastic differential equations; Stochastic partial differential equations

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Yeadon, C. (2015). Approximating solutions of backward doubly stochastic differential equations with measurable coefficients using a time discretization scheme. (Doctoral Dissertation). Loughborough University. Retrieved from https://dspace.lboro.ac.uk/2134/20643 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.682529

Chicago Manual of Style (16^th Edition):

Yeadon, Cyrus. “Approximating solutions of backward doubly stochastic differential equations with measurable coefficients using a time discretization scheme.” 2015. Doctoral Dissertation, Loughborough University. Accessed June 16, 2019. https://dspace.lboro.ac.uk/2134/20643 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.682529.

MLA Handbook (7^th Edition):

Yeadon, Cyrus. “Approximating solutions of backward doubly stochastic differential equations with measurable coefficients using a time discretization scheme.” 2015. Web. 16 Jun 2019.

Vancouver:

Yeadon C. Approximating solutions of backward doubly stochastic differential equations with measurable coefficients using a time discretization scheme. [Internet] [Doctoral dissertation]. Loughborough University; 2015. [cited 2019 Jun 16]. Available from: https://dspace.lboro.ac.uk/2134/20643 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.682529.

Council of Science Editors:

Yeadon C. Approximating solutions of backward doubly stochastic differential equations with measurable coefficients using a time discretization scheme. [Doctoral Dissertation]. Loughborough University; 2015. Available from: https://dspace.lboro.ac.uk/2134/20643 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.682529

University of Arizona

6. McDaniel, Austin James. The Effects of Time Delay on Noisy Systems .

Degree: 2015, University of Arizona

URL: http://hdl.handle.net/10150/556867

► We consider a general stochastic differential delay equation (SDDE) with multiplicative colored noise. We study the limit as the time delays and the correlation times… (more)

Subjects/Keywords: stochastic differential equations; time delay; Applied Mathematics; stochastic differential delay equations

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

McDaniel, A. J. (2015). The Effects of Time Delay on Noisy Systems . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/556867

Chicago Manual of Style (16^th Edition):

McDaniel, Austin James. “The Effects of Time Delay on Noisy Systems .” 2015. Doctoral Dissertation, University of Arizona. Accessed June 16, 2019. http://hdl.handle.net/10150/556867.

MLA Handbook (7^th Edition):

McDaniel, Austin James. “The Effects of Time Delay on Noisy Systems .” 2015. Web. 16 Jun 2019.

Vancouver:

McDaniel AJ. The Effects of Time Delay on Noisy Systems . [Internet] [Doctoral dissertation]. University of Arizona; 2015. [cited 2019 Jun 16]. Available from: http://hdl.handle.net/10150/556867.

Council of Science Editors:

McDaniel AJ. The Effects of Time Delay on Noisy Systems . [Doctoral Dissertation]. University of Arizona; 2015. Available from: http://hdl.handle.net/10150/556867

University of Rochester

7. Lin, Kevin. Hitting properties of a stochastic PDE.

Degree: PhD, 2017, University of Rochester

URL: http://hdl.handle.net/1802/33152

► In this thesis, we investigate the hitting properties of a class of stochastic partial diffierential equations (SPDEs). SPDEs are PDEs with stochastic terms, analogous to… (more)

Subjects/Keywords: Probability theory; Stochastic partial differential equations; Stochastic wave equations

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APA (6^th Edition):

Lin, K. (2017). Hitting properties of a stochastic PDE. (Doctoral Dissertation). University of Rochester. Retrieved from http://hdl.handle.net/1802/33152

Chicago Manual of Style (16^th Edition):

Lin, Kevin. “Hitting properties of a stochastic PDE.” 2017. Doctoral Dissertation, University of Rochester. Accessed June 16, 2019. http://hdl.handle.net/1802/33152.

MLA Handbook (7^th Edition):

Lin, Kevin. “Hitting properties of a stochastic PDE.” 2017. Web. 16 Jun 2019.

Vancouver:

Lin K. Hitting properties of a stochastic PDE. [Internet] [Doctoral dissertation]. University of Rochester; 2017. [cited 2019 Jun 16]. Available from: http://hdl.handle.net/1802/33152.

Council of Science Editors:

Lin K. Hitting properties of a stochastic PDE. [Doctoral Dissertation]. University of Rochester; 2017. Available from: http://hdl.handle.net/1802/33152

University of KwaZulu-Natal

8. [No author]. Applications of symmetry analysis of partial differential and stochastic differential equations arising from mathematics of finance.

Degree: Mathematics, 2011, University of KwaZulu-Natal

URL: http://hdl.handle.net/10413/9865

► In the standard modeling of the pricing of options and derivatives as generally understood these days the underlying process is taken to be a Wiener… (more)

▼ In the standard modeling of the pricing of options and derivatives as generally understood these days the underlying process is taken to be a Wiener Process or a Levy Process. The stochastic process is modeled as a stochastic differential equation. From this equation a partial differential equation is obtained by application of the Feynman-Kac Theorem. The resulting partial differential equation is of Hamilton-Jacobi-Bellman type. Analysis of the partial differential equations arising from Mathematics of Finance using the methods of the Lie Theory of Continuous Groups has been performed over the last twenty years, but it is only in recent years that there has been a concerted effort to make full use of the Lie theory. We propose an extension of Mahomed and Leach's (1990) formula for the nth-prolongation of an nth-order ordinary differential equation to the nth-prolongation of the generator of an hyperbolic partial differential equation with p dependent and k independent variables. The symmetry analysis of this partial differential equation shows that the associated Lie algebra is {sl(2,R)⊕W₃}⊕s ∞A₁ with 12 optimal systems. A modeling approach based upon stochastic volatility for modeling prices in the deregulated Pennsylvania State Electricity market is adopted for application. We propose a dynamic linear model (DLM) in which switching structure for the measurement matrix is incorporated into a two-state Gaussian mixture/first-order autoregressive (AR (1)) configuration in a nonstationary independent process defined by time-varying probabilities. The estimates of maximum likelihood of the parameters from the "modified" Kalman filter showed a significant mean-reversion rate of 0.9363 which translates to a half-life price of electricity of nine months. Associated with this mean-reversion is the high measure of price volatility at 35%. Within the last decade there has been some work done upon the symmetries of stochastic differential equations. Here empirical results contradict earliest normality hypotheses on log-return series in favour of asymmetry of the probability distribution describing the process. Using the Akaike Information Criterion (AIC) and the Log-likelihood estimation (LLH) methods as selection criteria, the normal inverse Gaussian (NIG) outperformed four other candidate probability distributions among the class of Generalized Hyperbolic (GH) distributions in describing the heavy tails present in the process. Similarly, the Skewed Student's t (SSt) is the best fit for Bonny Crude Oil and Natural Gas log-returns. The observed volatility measures of these three commodity prices were examined. The Weibull distribution gives the best fit both electricity and crude oil data while the Gamma distribution is selected for natural gas data in the volatility profiles among the five candidate probability density functions (Normal, Lognormal, Gamma, Inverse Gamma and the Inverse Gaussian) considered. Advisors/Committee Members: O'Hara, John G (advisor), Leach, Peter Gavin Lawrence (advisor).

Subjects/Keywords: Stochastic differential equations.; Differential equations, Partial.; Lie groups.; Mathematics.

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APA (6^th Edition):

author], [. (2011). Applications of symmetry analysis of partial differential and stochastic differential equations arising from mathematics of finance. (Thesis). University of KwaZulu-Natal. Retrieved from http://hdl.handle.net/10413/9865

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

author], [No. “Applications of symmetry analysis of partial differential and stochastic differential equations arising from mathematics of finance. ” 2011. Thesis, University of KwaZulu-Natal. Accessed June 16, 2019. http://hdl.handle.net/10413/9865.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

author], [No. “Applications of symmetry analysis of partial differential and stochastic differential equations arising from mathematics of finance. ” 2011. Web. 16 Jun 2019.

Vancouver:

author] [. Applications of symmetry analysis of partial differential and stochastic differential equations arising from mathematics of finance. [Internet] [Thesis]. University of KwaZulu-Natal; 2011. [cited 2019 Jun 16]. Available from: http://hdl.handle.net/10413/9865.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

author] [. Applications of symmetry analysis of partial differential and stochastic differential equations arising from mathematics of finance. [Thesis]. University of KwaZulu-Natal; 2011. Available from: http://hdl.handle.net/10413/9865

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Duke University

9. Thomas, Rachel Lee. Time-Scaled Stochastic Input to Biochemical Reaction Networks .

Degree: 2010, Duke University

URL: http://hdl.handle.net/10161/2443

► Biochemical reaction networks with a sufficiently large number of molecules may be represented as systems of differential equations. Many networks receive inputs that fluctuate… (more)

Subjects/Keywords: Mathematics; differential equations; multiple scales; reaction networks; stochastic differential equations

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APA (6^th Edition):

Thomas, R. L. (2010). Time-Scaled Stochastic Input to Biochemical Reaction Networks . (Thesis). Duke University. Retrieved from http://hdl.handle.net/10161/2443

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Thomas, Rachel Lee. “Time-Scaled Stochastic Input to Biochemical Reaction Networks .” 2010. Thesis, Duke University. Accessed June 16, 2019. http://hdl.handle.net/10161/2443.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Thomas, Rachel Lee. “Time-Scaled Stochastic Input to Biochemical Reaction Networks .” 2010. Web. 16 Jun 2019.

Vancouver:

Thomas RL. Time-Scaled Stochastic Input to Biochemical Reaction Networks . [Internet] [Thesis]. Duke University; 2010. [cited 2019 Jun 16]. Available from: http://hdl.handle.net/10161/2443.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Thomas RL. Time-Scaled Stochastic Input to Biochemical Reaction Networks . [Thesis]. Duke University; 2010. Available from: http://hdl.handle.net/10161/2443

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Ottawa

10. René, Alexandre. Spectral Solution Method for Distributed Delay Stochastic Differential Equations .

Degree: 2016, University of Ottawa

URL: http://hdl.handle.net/10393/34327

► Stochastic delay differential equations naturally arise in models of complex natural phenomena, yet continue to resist efforts to find analytical solutions to them: general solutions… (more)

Subjects/Keywords: stochastic differential equations; distributed delay differential equations; biorthogonal decomposition

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APA (6^th Edition):

René, A. (2016). Spectral Solution Method for Distributed Delay Stochastic Differential Equations . (Thesis). University of Ottawa. Retrieved from http://hdl.handle.net/10393/34327

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

René, Alexandre. “Spectral Solution Method for Distributed Delay Stochastic Differential Equations .” 2016. Thesis, University of Ottawa. Accessed June 16, 2019. http://hdl.handle.net/10393/34327.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

René, Alexandre. “Spectral Solution Method for Distributed Delay Stochastic Differential Equations .” 2016. Web. 16 Jun 2019.

Vancouver:

René A. Spectral Solution Method for Distributed Delay Stochastic Differential Equations . [Internet] [Thesis]. University of Ottawa; 2016. [cited 2019 Jun 16]. Available from: http://hdl.handle.net/10393/34327.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

René A. Spectral Solution Method for Distributed Delay Stochastic Differential Equations . [Thesis]. University of Ottawa; 2016. Available from: http://hdl.handle.net/10393/34327

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Alberta

11. Krasin, Vladislav. Comparison theorem and its applications to finance.

Degree: PhD, Department of Mathematical and Statistical Sciences, 2010, University of Alberta

URL: https://era.library.ualberta.ca/files/6w924d05r

► The current Thesis is devoted to comprehensive studies of comparison, or stochastic domination, theorems. It presents a combination of theoretical research and practical ideas formulated… (more)

Subjects/Keywords: Mathematical finance, stochastic differential equations, comparison theorem

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APA (6^th Edition):

Krasin, V. (2010). Comparison theorem and its applications to finance. (Doctoral Dissertation). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/6w924d05r

Chicago Manual of Style (16^th Edition):

Krasin, Vladislav. “Comparison theorem and its applications to finance.” 2010. Doctoral Dissertation, University of Alberta. Accessed June 16, 2019. https://era.library.ualberta.ca/files/6w924d05r.

MLA Handbook (7^th Edition):

Krasin, Vladislav. “Comparison theorem and its applications to finance.” 2010. Web. 16 Jun 2019.

Vancouver:

Krasin V. Comparison theorem and its applications to finance. [Internet] [Doctoral dissertation]. University of Alberta; 2010. [cited 2019 Jun 16]. Available from: https://era.library.ualberta.ca/files/6w924d05r.

Council of Science Editors:

Krasin V. Comparison theorem and its applications to finance. [Doctoral Dissertation]. University of Alberta; 2010. Available from: https://era.library.ualberta.ca/files/6w924d05r

12. Massoud, Mohammad. Statistical verification techniques for stochastic dynamic systems .

Degree: 2015, State University of New York at New Paltz

URL: http://hdl.handle.net/1951/66389

► Electronic chip design, aircraft stability, finance, economy and even our social life can be affected by random events. Noise is a random process that occurs… (more)

Subjects/Keywords: Stochastic differential equations; Dynamics; Noise; Nonlinear systems

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APA (6^th Edition):

Massoud, M. (2015). Statistical verification techniques for stochastic dynamic systems . (Thesis). State University of New York at New Paltz. Retrieved from http://hdl.handle.net/1951/66389

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Massoud, Mohammad. “Statistical verification techniques for stochastic dynamic systems .” 2015. Thesis, State University of New York at New Paltz. Accessed June 16, 2019. http://hdl.handle.net/1951/66389.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Massoud, Mohammad. “Statistical verification techniques for stochastic dynamic systems .” 2015. Web. 16 Jun 2019.

Vancouver:

Massoud M. Statistical verification techniques for stochastic dynamic systems . [Internet] [Thesis]. State University of New York at New Paltz; 2015. [cited 2019 Jun 16]. Available from: http://hdl.handle.net/1951/66389.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Massoud M. Statistical verification techniques for stochastic dynamic systems . [Thesis]. State University of New York at New Paltz; 2015. Available from: http://hdl.handle.net/1951/66389

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Manchester

13. Taylor, Phillip. Simulating Gaussian random fields and solving stochastic differential equations using bounded Wiener increments.

Degree: PhD, 2014, University of Manchester

URL: https://www.research.manchester.ac.uk/portal/en/theses/simulating-gaussian-random-fields-and-solving-stochastic-differential-equations-using-bounded-wiener-increments(b77a0fcc-3d86-46b2-8dbf-2a689d9f8f77).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603185

This thesis is in two parts. Part I concerns simulation of random fields using the circulant embedding method, and Part II studies the numerical solution of stochastic differential equations (SDEs).

Subjects/Keywords: 519.2; Stochastic Differential Equations; Random Fields

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APA (6^th Edition):

Taylor, P. (2014). Simulating Gaussian random fields and solving stochastic differential equations using bounded Wiener increments. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/simulating-gaussian-random-fields-and-solving-stochastic-differential-equations-using-bounded-wiener-increments(b77a0fcc-3d86-46b2-8dbf-2a689d9f8f77).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603185

Chicago Manual of Style (16^th Edition):

Taylor, Phillip. “Simulating Gaussian random fields and solving stochastic differential equations using bounded Wiener increments.” 2014. Doctoral Dissertation, University of Manchester. Accessed June 16, 2019. https://www.research.manchester.ac.uk/portal/en/theses/simulating-gaussian-random-fields-and-solving-stochastic-differential-equations-using-bounded-wiener-increments(b77a0fcc-3d86-46b2-8dbf-2a689d9f8f77).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603185.

MLA Handbook (7^th Edition):

Taylor, Phillip. “Simulating Gaussian random fields and solving stochastic differential equations using bounded Wiener increments.” 2014. Web. 16 Jun 2019.

Vancouver:

Taylor P. Simulating Gaussian random fields and solving stochastic differential equations using bounded Wiener increments. [Internet] [Doctoral dissertation]. University of Manchester; 2014. [cited 2019 Jun 16]. Available from: https://www.research.manchester.ac.uk/portal/en/theses/simulating-gaussian-random-fields-and-solving-stochastic-differential-equations-using-bounded-wiener-increments(b77a0fcc-3d86-46b2-8dbf-2a689d9f8f77).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603185.

Council of Science Editors:

Taylor P. Simulating Gaussian random fields and solving stochastic differential equations using bounded Wiener increments. [Doctoral Dissertation]. University of Manchester; 2014. Available from: https://www.research.manchester.ac.uk/portal/en/theses/simulating-gaussian-random-fields-and-solving-stochastic-differential-equations-using-bounded-wiener-increments(b77a0fcc-3d86-46b2-8dbf-2a689d9f8f77).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603185

Louisiana State University

14. Esunge, Julius. White noise methods for anticipating stochastic differential equations.

Degree: PhD, Applied Mathematics, 2009, Louisiana State University

URL: etd-07062009-094329 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2132

► This dissertation focuses on linear stochastic differential equations of anticipating type. Owing to the lack of a theory of differentiation for random processes, the said… (more)

Subjects/Keywords: White Noise; Anticipating; Stochastic Differential Equations

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APA (6^th Edition):

Esunge, J. (2009). White noise methods for anticipating stochastic differential equations. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-07062009-094329 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2132

Chicago Manual of Style (16^th Edition):

Esunge, Julius. “White noise methods for anticipating stochastic differential equations.” 2009. Doctoral Dissertation, Louisiana State University. Accessed June 16, 2019. etd-07062009-094329 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2132.

MLA Handbook (7^th Edition):

Esunge, Julius. “White noise methods for anticipating stochastic differential equations.” 2009. Web. 16 Jun 2019.

Vancouver:

Esunge J. White noise methods for anticipating stochastic differential equations. [Internet] [Doctoral dissertation]. Louisiana State University; 2009. [cited 2019 Jun 16]. Available from: etd-07062009-094329 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2132.

Council of Science Editors:

Esunge J. White noise methods for anticipating stochastic differential equations. [Doctoral Dissertation]. Louisiana State University; 2009. Available from: etd-07062009-094329 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2132

15. Zhao, Lin. Portfolio selection of stochastic differential equation with jumps under regime switching.

Degree: PhD, 2010, Swansea University

URL: https://cronfa.swan.ac.uk/Record/cronfa42401 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.678345

► In this thesis, we are interested in the stochastic differential equation with jumps under regime switching. Firstly, we investigate a continuous-time version of the mean-variance… (more)

Subjects/Keywords: 515; Portfolio selection; Stochastic differential equations

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APA (6^th Edition):

Zhao, L. (2010). Portfolio selection of stochastic differential equation with jumps under regime switching. (Doctoral Dissertation). Swansea University. Retrieved from https://cronfa.swan.ac.uk/Record/cronfa42401 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.678345

Chicago Manual of Style (16^th Edition):

Zhao, Lin. “Portfolio selection of stochastic differential equation with jumps under regime switching.” 2010. Doctoral Dissertation, Swansea University. Accessed June 16, 2019. https://cronfa.swan.ac.uk/Record/cronfa42401 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.678345.

MLA Handbook (7^th Edition):

Zhao, Lin. “Portfolio selection of stochastic differential equation with jumps under regime switching.” 2010. Web. 16 Jun 2019.

Vancouver:

Zhao L. Portfolio selection of stochastic differential equation with jumps under regime switching. [Internet] [Doctoral dissertation]. Swansea University; 2010. [cited 2019 Jun 16]. Available from: https://cronfa.swan.ac.uk/Record/cronfa42401 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.678345.

Council of Science Editors:

Zhao L. Portfolio selection of stochastic differential equation with jumps under regime switching. [Doctoral Dissertation]. Swansea University; 2010. Available from: https://cronfa.swan.ac.uk/Record/cronfa42401 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.678345

Columbia University

16. Dandapani, Aditi. Enlargement of Filtration and the Strict Local Martingale Property in Stochastic Differential Equations.

Degree: 2016, Columbia University

URL: https://doi.org/10.7916/D8XW4JZ2

► In this thesis, we study the strict local martingale property of solutions of various types of stochastic differential equations and the effect of an initial… (more)

Subjects/Keywords: Stochastic differential equations; Martingales (Mathematics); Mathematics

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APA (6^th Edition):

Dandapani, A. (2016). Enlargement of Filtration and the Strict Local Martingale Property in Stochastic Differential Equations. (Doctoral Dissertation). Columbia University. Retrieved from https://doi.org/10.7916/D8XW4JZ2

Chicago Manual of Style (16^th Edition):

Dandapani, Aditi. “Enlargement of Filtration and the Strict Local Martingale Property in Stochastic Differential Equations.” 2016. Doctoral Dissertation, Columbia University. Accessed June 16, 2019. https://doi.org/10.7916/D8XW4JZ2.

MLA Handbook (7^th Edition):

Dandapani, Aditi. “Enlargement of Filtration and the Strict Local Martingale Property in Stochastic Differential Equations.” 2016. Web. 16 Jun 2019.

Vancouver:

Dandapani A. Enlargement of Filtration and the Strict Local Martingale Property in Stochastic Differential Equations. [Internet] [Doctoral dissertation]. Columbia University; 2016. [cited 2019 Jun 16]. Available from: https://doi.org/10.7916/D8XW4JZ2.

Council of Science Editors:

Dandapani A. Enlargement of Filtration and the Strict Local Martingale Property in Stochastic Differential Equations. [Doctoral Dissertation]. Columbia University; 2016. Available from: https://doi.org/10.7916/D8XW4JZ2

University of Southern California

17. Chen, Jianfu. Forward-backward stochastic differential equations with discontinuous coefficient and regime switching term structure model.

Degree: PhD, Applied Mathematics, 2011, University of Southern California

URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/444005/rec/2876

► In this dissertation, we propose a regime switch term structure model built as forward-backward stochastic differential equations. We first generalize the model and study the… (more)

Subjects/Keywords: discontinuous coefficient; regime switching; stochastic differential equations

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APA (6^th Edition):

Chen, J. (2011). Forward-backward stochastic differential equations with discontinuous coefficient and regime switching term structure model. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/444005/rec/2876

Chicago Manual of Style (16^th Edition):

Chen, Jianfu. “Forward-backward stochastic differential equations with discontinuous coefficient and regime switching term structure model.” 2011. Doctoral Dissertation, University of Southern California. Accessed June 16, 2019. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/444005/rec/2876.

MLA Handbook (7^th Edition):

Chen, Jianfu. “Forward-backward stochastic differential equations with discontinuous coefficient and regime switching term structure model.” 2011. Web. 16 Jun 2019.

Vancouver:

Chen J. Forward-backward stochastic differential equations with discontinuous coefficient and regime switching term structure model. [Internet] [Doctoral dissertation]. University of Southern California; 2011. [cited 2019 Jun 16]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/444005/rec/2876.

Council of Science Editors:

Chen J. Forward-backward stochastic differential equations with discontinuous coefficient and regime switching term structure model. [Doctoral Dissertation]. University of Southern California; 2011. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/444005/rec/2876

Michigan State University

18. Huang, Liying. Stochastic differential equations and their numerical approximations.

Degree: PhD, Department of Mathematics, 1995, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:29961

Subjects/Keywords: Stochastic differential equations

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APA (6^th Edition):

Huang, L. (1995). Stochastic differential equations and their numerical approximations. (Doctoral Dissertation). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:29961

Chicago Manual of Style (16^th Edition):

Huang, Liying. “Stochastic differential equations and their numerical approximations.” 1995. Doctoral Dissertation, Michigan State University. Accessed June 16, 2019. http://etd.lib.msu.edu/islandora/object/etd:29961.

MLA Handbook (7^th Edition):

Huang, Liying. “Stochastic differential equations and their numerical approximations.” 1995. Web. 16 Jun 2019.

Vancouver:

Huang L. Stochastic differential equations and their numerical approximations. [Internet] [Doctoral dissertation]. Michigan State University; 1995. [cited 2019 Jun 16]. Available from: http://etd.lib.msu.edu/islandora/object/etd:29961.

Council of Science Editors:

Huang L. Stochastic differential equations and their numerical approximations. [Doctoral Dissertation]. Michigan State University; 1995. Available from: http://etd.lib.msu.edu/islandora/object/etd:29961

University of Edinburgh

19. Dareiotis, Anastasios Constantinos. Stochastic partial differential and integro-differential equations.

Degree: PhD, 2015, University of Edinburgh

URL: http://hdl.handle.net/1842/14186

► In this work we present some new results concerning stochastic partial differential and integro-differential equations (SPDEs and SPIDEs) that appear in non-linear filtering. We prove… (more)

Subjects/Keywords: 519.2; stochastic partial differential equations; stochastic partial integro-differential equations; SPDEs; SPIDEs

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APA (6^th Edition):

Dareiotis, A. C. (2015). Stochastic partial differential and integro-differential equations. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/14186

Chicago Manual of Style (16^th Edition):

Dareiotis, Anastasios Constantinos. “Stochastic partial differential and integro-differential equations.” 2015. Doctoral Dissertation, University of Edinburgh. Accessed June 16, 2019. http://hdl.handle.net/1842/14186.

MLA Handbook (7^th Edition):

Dareiotis, Anastasios Constantinos. “Stochastic partial differential and integro-differential equations.” 2015. Web. 16 Jun 2019.

Vancouver:

Dareiotis AC. Stochastic partial differential and integro-differential equations. [Internet] [Doctoral dissertation]. University of Edinburgh; 2015. [cited 2019 Jun 16]. Available from: http://hdl.handle.net/1842/14186.

Council of Science Editors:

Dareiotis AC. Stochastic partial differential and integro-differential equations. [Doctoral Dissertation]. University of Edinburgh; 2015. Available from: http://hdl.handle.net/1842/14186

University of Alberta

20. Deng, Jian. Uncertainty Quantification of Dynamical Systems and Stochastic Symplectic Schemes.

Degree: PhD, Department of Mathematical and Statistical Sciences, 2013, University of Alberta

URL: https://era.library.ualberta.ca/files/n583xv59r

► It has been known that for some physical problems, a small change in the system parameters or in the initial/boundary conditions could leas to a… (more)

▼ It has been known that for some physical problems, a small change in the system parameters or in the initial/boundary conditions could leas to a significant change in the system response. Hence, it is of importance to investigate the impact of uncertainty on dynamical system in order to fully understand the system behavior. In this thesis, numerical methods used to simulate the effect of random/stochastic perturbation on dynamical systems are studied. In the first part of this thesis, an aeroelastic system model representing an oscillating airfoil in pitch and plunge with random variations in the flow speed, the structural stiffness terms and initial conditions are concerned. Two approaches, stochastic normal form and stochastic collocation method, are proposed to investigate the Hopf bifurcation and the secondary bifurcation behavior, respectively. Stochastic normal form allows us to study analytically the Hopf bifurcation scenario and to predict the amplitude and frequency of the limit cycle oscillation; while numerical simulations demonstrate the effectiveness of stochastic collocation method for long term computation and discontinuous problems. In the second part of this work, we focus the construction of efficient and robust computational schemes for stochastic system, and the stochastic symplectic schemes for stochastic Hamiltonian system are developed. A systematic procedure to construct symplectic numerical schemes for stochastic Hamiltonian systems is presented. The approach is an extension to the stochastic case of the methods based on generating functions. The idea is also extended to the symplectic weak scheme construction. Theoretical analysis of the convergence is reported for strong/weak symplectic integrators. The numerical simulations are carried out to confirm that the symplectic methods are efficient computational tools for long-term behaviors. Moreover, the coefficients of the generating function are invariant under permutations for the stochastic Hamiltonian system preserving Hamiltonian functions. As a consequence the high-order symplectic weak and strong methods have simpler forms than the Taylor expansion schemes with the same order.

Subjects/Keywords: stochastic symplectic integrator; Uncertainty Quantification; Stochastic differential equations

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APA (6^th Edition):

Deng, J. (2013). Uncertainty Quantification of Dynamical Systems and Stochastic Symplectic Schemes. (Doctoral Dissertation). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/n583xv59r

Chicago Manual of Style (16^th Edition):

Deng, Jian. “Uncertainty Quantification of Dynamical Systems and Stochastic Symplectic Schemes.” 2013. Doctoral Dissertation, University of Alberta. Accessed June 16, 2019. https://era.library.ualberta.ca/files/n583xv59r.

MLA Handbook (7^th Edition):

Deng, Jian. “Uncertainty Quantification of Dynamical Systems and Stochastic Symplectic Schemes.” 2013. Web. 16 Jun 2019.

Vancouver:

Deng J. Uncertainty Quantification of Dynamical Systems and Stochastic Symplectic Schemes. [Internet] [Doctoral dissertation]. University of Alberta; 2013. [cited 2019 Jun 16]. Available from: https://era.library.ualberta.ca/files/n583xv59r.

Council of Science Editors:

Deng J. Uncertainty Quantification of Dynamical Systems and Stochastic Symplectic Schemes. [Doctoral Dissertation]. University of Alberta; 2013. Available from: https://era.library.ualberta.ca/files/n583xv59r

University of Rochester

21. Henao, Alejandro Gomez (1983 - ). Uniqueness properties in the theory of stochastic differential equations.

Degree: PhD, 2013, University of Rochester

URL: http://hdl.handle.net/1802/26859

► The theory of stochastic differential equations (SDE) describes the world using differential equations, including randomness as a fundamental factor. This theory integrates randomness into the… (more)

Subjects/Keywords: Binary matrices; Stochastic differential equations; Stochastic processes; Uniqueness

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APA (6^th Edition):

Henao, A. G. (. -. ). (2013). Uniqueness properties in the theory of stochastic differential equations. (Doctoral Dissertation). University of Rochester. Retrieved from http://hdl.handle.net/1802/26859

Chicago Manual of Style (16^th Edition):

Henao, Alejandro Gomez (1983 - ). “Uniqueness properties in the theory of stochastic differential equations.” 2013. Doctoral Dissertation, University of Rochester. Accessed June 16, 2019. http://hdl.handle.net/1802/26859.

MLA Handbook (7^th Edition):

Henao, Alejandro Gomez (1983 - ). “Uniqueness properties in the theory of stochastic differential equations.” 2013. Web. 16 Jun 2019.

Vancouver:

Henao AG(-). Uniqueness properties in the theory of stochastic differential equations. [Internet] [Doctoral dissertation]. University of Rochester; 2013. [cited 2019 Jun 16]. Available from: http://hdl.handle.net/1802/26859.

Council of Science Editors:

Henao AG(-). Uniqueness properties in the theory of stochastic differential equations. [Doctoral Dissertation]. University of Rochester; 2013. Available from: http://hdl.handle.net/1802/26859

Georgia Tech

22. Exarchos, Ioannis. Stochastic optimal control - a forward and backward sampling approach.

Degree: PhD, Aerospace Engineering, 2017, Georgia Tech

URL: http://hdl.handle.net/1853/59263

► Stochastic optimal control has seen significant recent development, motivated by its success in a plethora of engineering applications, such as autonomous systems, robotics, neuroscience, and… (more)

▼ Stochastic optimal control has seen significant recent development, motivated by its success in a plethora of engineering applications, such as autonomous systems, robotics, neuroscience, and financial engineering. Despite the many theoretical and algorithmic advancements that made such a success possible, several obstacles remain; most notable are (i) the mitigation of the curse of dimensionality inherent in optimal control problems, (ii) the design of efficient algorithms that allow for fast, online computation, and (iii) the expansion of the class of optimal control problems that can be addressed by algorithms in engineering practice. The aim of this dissertation is the development of a learning stochastic control framework which capitalizes on the innate relationship between certain nonlinear partial differential equations (PDEs) and forward and backward stochastic differential equations (FBSDEs), demonstrated by a nonlinear version of the Feynman-Kac lemma. By means of this lemma, we are able to obtain a probabilistic representation of the solution to the nonlinear Hamilton-Jacobi-Bellman PDE, expressed in form of a system of decoupled FBSDEs. This system of FBSDEs can then be simulated by employing linear regression techniques. We present a novel discretization scheme for FBSDEs, and enhance the resulting algorithm with importance sampling, thereby constructing an iterative scheme that is capable of learning the optimal control without an initial guess, even in systems with highly nonlinear, underactuated dynamics. The framework we develop within this dissertation addresses several classes of stochastic optimal control, such as L2, L1, risk sensitive control, as well as some classes of differential games, in both fixed-final-time as well as first-exit settings. Advisors/Committee Members: Tsiotras, Panagiotis (advisor), Theodorou, Evangelos A. (advisor), Haddad, Wassim M. (committee member), Zhou, Haomin (committee member), Popescu, Ionel (committee member).

Subjects/Keywords: Stochastic optimal control; Forward and backward stochastic differential equations

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APA (6^th Edition):

Exarchos, I. (2017). Stochastic optimal control - a forward and backward sampling approach. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/59263

Chicago Manual of Style (16^th Edition):

Exarchos, Ioannis. “Stochastic optimal control - a forward and backward sampling approach.” 2017. Doctoral Dissertation, Georgia Tech. Accessed June 16, 2019. http://hdl.handle.net/1853/59263.

MLA Handbook (7^th Edition):

Exarchos, Ioannis. “Stochastic optimal control - a forward and backward sampling approach.” 2017. Web. 16 Jun 2019.

Vancouver:

Exarchos I. Stochastic optimal control - a forward and backward sampling approach. [Internet] [Doctoral dissertation]. Georgia Tech; 2017. [cited 2019 Jun 16]. Available from: http://hdl.handle.net/1853/59263.

Council of Science Editors:

Exarchos I. Stochastic optimal control - a forward and backward sampling approach. [Doctoral Dissertation]. Georgia Tech; 2017. Available from: http://hdl.handle.net/1853/59263

University of Edinburgh

23. Zhang, Xiling. On numerical approximations for stochastic differential equations.

Degree: PhD, 2017, University of Edinburgh

URL: http://hdl.handle.net/1842/28931

► This thesis consists of several problems concerning numerical approximations for stochastic differential equations, and is divided into three parts. The first one is on the… (more)

Subjects/Keywords: stochastic differential equations; Lyapunov functions; asymptotic stability; Lévy processes; stochastic integrals

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APA (6^th Edition):

Zhang, X. (2017). On numerical approximations for stochastic differential equations. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/28931

Chicago Manual of Style (16^th Edition):

Zhang, Xiling. “On numerical approximations for stochastic differential equations.” 2017. Doctoral Dissertation, University of Edinburgh. Accessed June 16, 2019. http://hdl.handle.net/1842/28931.

MLA Handbook (7^th Edition):

Zhang, Xiling. “On numerical approximations for stochastic differential equations.” 2017. Web. 16 Jun 2019.

Vancouver:

Zhang X. On numerical approximations for stochastic differential equations. [Internet] [Doctoral dissertation]. University of Edinburgh; 2017. [cited 2019 Jun 16]. Available from: http://hdl.handle.net/1842/28931.

Council of Science Editors:

Zhang X. On numerical approximations for stochastic differential equations. [Doctoral Dissertation]. University of Edinburgh; 2017. Available from: http://hdl.handle.net/1842/28931

Stellenbosch University

24. Ndounkeu, Ludovic Tangpi. Optimal cross hedging of Insurance derivatives using quadratic BSDEs.

Degree: MSc, Mathematical Sciences, 2011, Stellenbosch University

URL: http://hdl.handle.net/10019.1/17950

►

ENGLISH ABSTRACT: We consider the utility portfolio optimization problem of an investor whose activities are influenced by an exogenous financial risk (like bad weather or… (more)

▼

ENGLISH ABSTRACT: We consider the utility portfolio optimization problem of an investor whose activities are influenced by an exogenous financial risk (like bad weather or energy shortage) in an incomplete financial market. We work with a fairly general non-Markovian model, allowing stochastic correlations between the underlying assets. This important problem in finance and insurance is tackled by means of backward stochastic differential equations (BSDEs), which have been shown to be powerful tools in stochastic control. To lay stress on the importance and the omnipresence of BSDEs in stochastic control, we present three methods to transform the control problem into a BSDEs. Namely, the martingale optimality principle introduced by Davis, the martingale representation and a method based on Itô-Ventzell’s formula. These approaches enable us to work with portfolio constraints described by closed, not necessarily convex sets and to get around the classical duality theory of convex analysis. The solution of the optimization problem can then be simply read from the solution of the BSDE. An interesting feature of each of the different approaches is that the generator of the BSDE characterizing the control problem has a quadratic growth and depends on the form of the set of constraints. We review some recent advances on the theory of quadratic BSDEs and its applications. There is no general existence result for multidimensional quadratic BSDEs. In the one-dimensional case, existence and uniqueness strongly depend on the form of the terminal condition. Other topics of investigation are measure solutions of BSDEs, notably measure solutions of BSDE with jumps and numerical approximations. We extend the equivalence result of Ankirchner et al. (2009) between existence of classical solutions and existence of measure solutions to the case of BSDEs driven by a Poisson process with a bounded terminal condition. We obtain a numerical scheme to approximate measure solutions. In fact, the existing self-contained construction of measure solutions gives rise to a numerical scheme for some classes of Lipschitz BSDEs. Two numerical schemes for quadratic BSDEs introduced in Imkeller et al. (2010) and based, respectively, on the Cole-Hopf transformation and the truncation procedure are implemented and the results are compared. Keywords: BSDE, quadratic growth, measure solutions, martingale theory, numerical scheme, indifference pricing and hedging, non-tradable underlying, defaultable claim, utility maximization.

AFRIKAANSE OPSOMMING: Ons beskou die nuts portefeulje optimalisering probleem van ’n belegger wat se aktiwiteite beïnvloed word deur ’n eksterne finansiele risiko (soos onweer of ’n energie tekort) in ’n onvolledige finansiële mark. Ons werk met ’n redelik algemene nie-Markoviaanse model, wat stogastiese korrelasies tussen die onderliggende bates toelaat. Hierdie belangrike probleem in finansies en versekering is aangepak deur middel van terugwaartse stogastiese differensiaalvergelykings …

Advisors/Committee Members: Ghomrasni, Raouf, Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences..

Subjects/Keywords: Mathematics; Backward stochastic differential equations; Stochastic control; Insurance derivatives; Cross hedging

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APA (6^th Edition):

Ndounkeu, L. T. (2011). Optimal cross hedging of Insurance derivatives using quadratic BSDEs. (Masters Thesis). Stellenbosch University. Retrieved from http://hdl.handle.net/10019.1/17950

Chicago Manual of Style (16^th Edition):

Ndounkeu, Ludovic Tangpi. “Optimal cross hedging of Insurance derivatives using quadratic BSDEs.” 2011. Masters Thesis, Stellenbosch University. Accessed June 16, 2019. http://hdl.handle.net/10019.1/17950.

MLA Handbook (7^th Edition):

Ndounkeu, Ludovic Tangpi. “Optimal cross hedging of Insurance derivatives using quadratic BSDEs.” 2011. Web. 16 Jun 2019.

Vancouver:

Ndounkeu LT. Optimal cross hedging of Insurance derivatives using quadratic BSDEs. [Internet] [Masters thesis]. Stellenbosch University; 2011. [cited 2019 Jun 16]. Available from: http://hdl.handle.net/10019.1/17950.

Council of Science Editors:

Ndounkeu LT. Optimal cross hedging of Insurance derivatives using quadratic BSDEs. [Masters Thesis]. Stellenbosch University; 2011. Available from: http://hdl.handle.net/10019.1/17950

University of New South Wales

25. Roberts, Dale. Equations with Boundary Noise.

Degree: Mathematics & Statistics, 2011, University of New South Wales

URL: http://handle.unsw.edu.au/1959.4/51637 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:10304/SOURCE02?view=true

► In 1993, Da Prato and Zabczyk showed that if one considers the heat equation on the interval (0,1) with white noise Dirichlet boundary conditions then… (more)

▼ In 1993, Da Prato and Zabczyk showed that if one considers the heat equation on the interval (0,1) with white noise Dirichlet boundary conditions then a function-valued mild solution cannot be obtained. In this thesis, we revisit this 'Dirichlet boundary noise problem'. First, we return the deterministic situation and extend the approach of Lasiecka and Balakrishan to the Banach setting to provide a point of comparison for the stochastic case. We then construct an equivalent stochastic theory and show that we cannot obtain Lp- valued solutions. Next we extend to higher-dimensions the idea of Alos and Bonaccorsi: function-valued solutions can be obtained on the half-line if considered in an appropriate weighted Lp space. We also show that a dichotomy is obtained: either a process is obtained on the weighted space or boundary values are understood in terms of traces, but not both. We also study the properties of the Dirichlet heat semigroup on weighted spaces in an attempt to build a foundation for the semigroup approach. Next, from the desire to understand the 'Dirichlet map' of random boundary data we move to the unit disk and perform a stochastic extension of some classic harmonic analysis results. This leads us to work with harmonic Hardy spaces and to consider radial and non-tangential convergence towards the boundary, to obtain an interesting representation theorem, and to finally reconnect our results with weighted spaces. Returning to our problem, we conclude that harmonic Hardy spaces are 'too small' to consider the white noise boundary data. Therefore, what is the appropriate space? We consider this question from two angles. First we take a larger space, specifically the Bloch space, and show that it may be an appropriate place to consider these dynamics. We then extend Makarov's LIL theorem to our stochastic case which gives a rate of blow-up near the boundary of our harmonic random field. We conclude that although the random Bloch dynamics are very interesting, we still do not have clear relationship with the boundary data but only an "inside-out" viewpoint. This inspires a "outside-in" approach whereby, due to a simple representation, we start with the white-noise data on the boundary and moving inwards we show rates of blow-up near typical and exceptional points. Finally, we show how these concepts may be extended to more general situations to provide a framework for understanding the local spatial dynamics of SPDE. Advisors/Committee Members: Dooley, Anthony, Mathematics & Statistics, Faculty of Science, UNSW.

Subjects/Keywords: Weighted spaces; Stochastic partial differential equations; Gaussian random fields; Stochastic evolution equations

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Roberts, D. (2011). Equations with Boundary Noise. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/51637 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:10304/SOURCE02?view=true

Chicago Manual of Style (16^th Edition):

Roberts, Dale. “Equations with Boundary Noise.” 2011. Doctoral Dissertation, University of New South Wales. Accessed June 16, 2019. http://handle.unsw.edu.au/1959.4/51637 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:10304/SOURCE02?view=true.

MLA Handbook (7^th Edition):

Roberts, Dale. “Equations with Boundary Noise.” 2011. Web. 16 Jun 2019.

Vancouver:

Roberts D. Equations with Boundary Noise. [Internet] [Doctoral dissertation]. University of New South Wales; 2011. [cited 2019 Jun 16]. Available from: http://handle.unsw.edu.au/1959.4/51637 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:10304/SOURCE02?view=true.

Council of Science Editors:

Roberts D. Equations with Boundary Noise. [Doctoral Dissertation]. University of New South Wales; 2011. Available from: http://handle.unsw.edu.au/1959.4/51637 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:10304/SOURCE02?view=true

University of Kansas

26. Liu, Yanghui. Numerical solutions of rough differential equations and stochastic differential equations.

Degree: PhD, Mathematics, 2016, University of Kansas

URL: http://hdl.handle.net/1808/21866

► In this dissertation, we investigate time-discrete numerical approximation schemes for rough differential equations and stochastic differential equations (SDE) driven by fractional Brownian motions (fBm). The… (more)

Subjects/Keywords: Mathematics; fourth moment theorem; fractional Brownian motions; Numerical solutions; rough differential equations; stochastic differential equations

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Liu, Y. (2016). Numerical solutions of rough differential equations and stochastic differential equations. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/21866

Chicago Manual of Style (16^th Edition):

Liu, Yanghui. “Numerical solutions of rough differential equations and stochastic differential equations.” 2016. Doctoral Dissertation, University of Kansas. Accessed June 16, 2019. http://hdl.handle.net/1808/21866.

MLA Handbook (7^th Edition):

Liu, Yanghui. “Numerical solutions of rough differential equations and stochastic differential equations.” 2016. Web. 16 Jun 2019.

Vancouver:

Liu Y. Numerical solutions of rough differential equations and stochastic differential equations. [Internet] [Doctoral dissertation]. University of Kansas; 2016. [cited 2019 Jun 16]. Available from: http://hdl.handle.net/1808/21866.

Council of Science Editors:

Liu Y. Numerical solutions of rough differential equations and stochastic differential equations. [Doctoral Dissertation]. University of Kansas; 2016. Available from: http://hdl.handle.net/1808/21866

University of Manchester

27. Yue, Wen. Absolute continuity of the laws, existence and uniqueness of solutions of some SDEs and SPDEs.

Degree: PhD, 2014, University of Manchester

URL: https://www.research.manchester.ac.uk/portal/en/theses/absolute-continuity-of-the-laws-existence-and-uniqueness-of-solutions-of-some-sdes-and-spdes(2bc80de8-7c36-453f-a7c2-69fa4ee0e705).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603266

► This thesis consists of four parts. In the first part we recall some background theory that will be used throughout the thesis. In the second… (more)

Subjects/Keywords: 519.2; Stochastic differential equations; Stochastic partial differential equations; Diffusion processes; Peturbed diffusion processes; Reflecting walls;

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APA (6^th Edition):

Yue, W. (2014). Absolute continuity of the laws, existence and uniqueness of solutions of some SDEs and SPDEs. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/absolute-continuity-of-the-laws-existence-and-uniqueness-of-solutions-of-some-sdes-and-spdes(2bc80de8-7c36-453f-a7c2-69fa4ee0e705).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603266

Chicago Manual of Style (16^th Edition):

Yue, Wen. “Absolute continuity of the laws, existence and uniqueness of solutions of some SDEs and SPDEs.” 2014. Doctoral Dissertation, University of Manchester. Accessed June 16, 2019. https://www.research.manchester.ac.uk/portal/en/theses/absolute-continuity-of-the-laws-existence-and-uniqueness-of-solutions-of-some-sdes-and-spdes(2bc80de8-7c36-453f-a7c2-69fa4ee0e705).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603266.

MLA Handbook (7^th Edition):

Yue, Wen. “Absolute continuity of the laws, existence and uniqueness of solutions of some SDEs and SPDEs.” 2014. Web. 16 Jun 2019.

Vancouver:

Yue W. Absolute continuity of the laws, existence and uniqueness of solutions of some SDEs and SPDEs. [Internet] [Doctoral dissertation]. University of Manchester; 2014. [cited 2019 Jun 16]. Available from: https://www.research.manchester.ac.uk/portal/en/theses/absolute-continuity-of-the-laws-existence-and-uniqueness-of-solutions-of-some-sdes-and-spdes(2bc80de8-7c36-453f-a7c2-69fa4ee0e705).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603266.

Council of Science Editors:

Yue W. Absolute continuity of the laws, existence and uniqueness of solutions of some SDEs and SPDEs. [Doctoral Dissertation]. University of Manchester; 2014. Available from: https://www.research.manchester.ac.uk/portal/en/theses/absolute-continuity-of-the-laws-existence-and-uniqueness-of-solutions-of-some-sdes-and-spdes(2bc80de8-7c36-453f-a7c2-69fa4ee0e705).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603266

University of Oxford

28. Liu, Xuan. Some contribution to analysis and stochastic analysis.

Degree: PhD, 2018, University of Oxford

URL: http://ora.ox.ac.uk/objects/uuid:485474c0-2501-4ef0-a0bc-492e5c6c9d62 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.757850

► The dissertation consists of two parts. The first part (Chapter 1 to 4) is on some contributions to the development of a non-linear analysis on… (more)

▼ The dissertation consists of two parts. The first part (Chapter 1 to 4) is on some contributions to the development of a non-linear analysis on the quintessential fractal set Sierpinski gasket and its probabilistic interpretation. The second part (Chapter 5) is on the asymptotic tail decays for suprema of stochastic processes satisfying certain conditional increment controls. Chapters 1, 2 and 3 are devoted to the establishment of a theory of backward problems for non-linear stochastic differential equations on the gasket, and to derive a probabilistic representation to some parabolic type partial differential equations on the gasket. In Chapter 2, using the theory of Markov processes, we derive the existence and uniqueness of solutions to backward stochastic differential equations driven by Brownian motion on the Sierpinski gasket, for which the major technical difficulty is the exponential integrability of quadratic processes of martingale additive functionals. A Feynman-Kac type representation is obtained as an application. In Chapter 3, we study the stochastic optimal control problems for which the system uncertainties come from Brownian motion on the gasket, and derive a stochastic maximum principle. It turns out that the necessary condition for optimal control problems on the gasket consists of two equations, in contrast to the classical result on ℝ^d, where the necessary condition is given by a single equation. The materials in Chapter 2 are based on a joint work with Zhongmin Qian (referenced in Chapter 2). Chapter 4 is devoted to the analytic study of some parabolic PDEs on the gasket. Using a new type of Sobolev inequality which involves singular measures developed in Section 4.2, we establish the existence and uniqueness of solutions to these PDEs, and derive the space-time regularity for solutions. As an interesting application of the results in Chapter 4 and the probabilistic representation developed in Chapter 2, we further study Burgers equations on the gasket, to which the space-time regularity for solutions is deduced. The materials in Chapter 4 are based on a joint work with Zhongmin Qian (referenced in Chapter 4). In Chapter 5, we consider a class of continuous stochastic processes which satisfy the conditional increment control condition. Typical examples include continuous martingales, fractional Brownian motions, and diffusions governed by SDEs. For such processes, we establish a Doob type maximal inequality. Under additional assumptions on the tail decays of their marginal distributions, we derive an estimate for the tail decay of the suprema (Theorem 5.3.2), which states that the suprema decays in a manner similar to the margins of the processes. In Section 5.4, as an application of Theorem 5.3.2, we derive the existence of strong solutions to a class of SDEs. The materials in this chapter is based on the work [44] by the author (Section 5.2 and Section 5.3) and an ongoing joint project with Guangyu Xi (Section 5.4).

Subjects/Keywords: Mathematics; Stochastic Analysis; Singular measures; Sobolev inequalities; Backward stochastic differential equations; Sierpinski gasket; Semi-linear partial differential equations

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APA (6^th Edition):

Liu, X. (2018). Some contribution to analysis and stochastic analysis. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:485474c0-2501-4ef0-a0bc-492e5c6c9d62 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.757850

Chicago Manual of Style (16^th Edition):

Liu, Xuan. “Some contribution to analysis and stochastic analysis.” 2018. Doctoral Dissertation, University of Oxford. Accessed June 16, 2019. http://ora.ox.ac.uk/objects/uuid:485474c0-2501-4ef0-a0bc-492e5c6c9d62 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.757850.

MLA Handbook (7^th Edition):

Liu, Xuan. “Some contribution to analysis and stochastic analysis.” 2018. Web. 16 Jun 2019.

Vancouver:

Liu X. Some contribution to analysis and stochastic analysis. [Internet] [Doctoral dissertation]. University of Oxford; 2018. [cited 2019 Jun 16]. Available from: http://ora.ox.ac.uk/objects/uuid:485474c0-2501-4ef0-a0bc-492e5c6c9d62 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.757850.

Council of Science Editors:

Liu X. Some contribution to analysis and stochastic analysis. [Doctoral Dissertation]. University of Oxford; 2018. Available from: http://ora.ox.ac.uk/objects/uuid:485474c0-2501-4ef0-a0bc-492e5c6c9d62 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.757850

29. Hofmanová, Martina. Degenerate parabolic stochastic partial differential equations : Équations aux dérivées partielles stochastiques paraboliques dégénérées.

Degree: Docteur es, Mathématiques, 2013, Cachan, Ecole normale supérieure; Charles University. Faculty of mathematics and physics. Department of metal physics (Prague)

URL: http://www.theses.fr/2013DENS0024

►

Dans cette thèse, on considère des problèmes issus de l'analyse d'EDP stochastiques paraboliques non-dégénérées et dégénérées, de lois de conservation hyperboliques stochastiques, et d'EDS avec… (more)

▼

Dans cette thèse, on considère des problèmes issus de l'analyse d'EDP stochastiques paraboliques non-dégénérées et dégénérées, de lois de conservation hyperboliques stochastiques, et d'EDS avec coefficients continus. Dans une première partie, on s'intéresse à des EDPS paraboliques dégénérées- on adapte les notions de formulation et de solutions cinétiques, puis on établit l'existence, l'unicité ainsi que la dépendance continu en la condition initiale. Comme résultat préliminaire, on obtient la régularité des solutions dans le cas non-dégénéré, sous l'hypothèse que les coefficients sont suffisamment réguliers et ont des dérivées bornées. Dans une deuxième partie, on considère des lois de conservation hyperboliques avec un forçage stochastique, et on étudie leur approximation au sens de Bhatnagar-Gross-Krook. En particulier, on décrit les lois de conservation comme limites hydrodynamiques du modèle BGK stochastique lorsque le paramètre d'échelle microscopique tend vers 0. Dans une troisième partie, on donne une preuve nouvelle et élémentaire du théorème classique de Skorokhod, concernant l'existence de solutions faibles d'EDS à coefficients continus, sous une condition de type Lyapunov appropriée.

In this thesis, we address several problems arising in the study of nondegenerate and degenerate parabolic SPDEs, stochastic hyperbolic conservation laws and SDEs with continues coefficients. In the first part, we are interested in degenerate parabolic SPDEs, adapt the notion of kinetic formulation and kinetic solution and establish existence, uniqueness as well as continuous dependence on initial data. As a preliminary result we obtain regularity of solutions in the nondegenerate case under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives. In the second part, we consider hyperbolic conservation laws with stochastic forcing and study their approximations in the sense of Bhatnagar-Gross-Krook. In particular, we describe the conservation laws as a hydrodynamic limit of the stochastic BGK model as the microscopic scale vanishes. In the last part, we provide a new and fairly elementary proof of Skorkhod's classical theorem on existence of weak solutions to SDEs with continuous coefficients satisfying a suitable Lyapunov condition.

Advisors/Committee Members: Debussche, Arnaud (thesis director), Seidler, Jan (thesis director).

Subjects/Keywords: Équations aux dérivées partielles stochastiques; Équations différentielles stochastiques; Solutions cinétiques; Stochastic partial differential equations; Stochastic differential equations; Kinetic solutions

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Hofmanová, M. (2013). Degenerate parabolic stochastic partial differential equations : Équations aux dérivées partielles stochastiques paraboliques dégénérées. (Doctoral Dissertation). Cachan, Ecole normale supérieure; Charles University. Faculty of mathematics and physics. Department of metal physics (Prague). Retrieved from http://www.theses.fr/2013DENS0024

Chicago Manual of Style (16^th Edition):

Hofmanová, Martina. “Degenerate parabolic stochastic partial differential equations : Équations aux dérivées partielles stochastiques paraboliques dégénérées.” 2013. Doctoral Dissertation, Cachan, Ecole normale supérieure; Charles University. Faculty of mathematics and physics. Department of metal physics (Prague). Accessed June 16, 2019. http://www.theses.fr/2013DENS0024.

MLA Handbook (7^th Edition):

Hofmanová, Martina. “Degenerate parabolic stochastic partial differential equations : Équations aux dérivées partielles stochastiques paraboliques dégénérées.” 2013. Web. 16 Jun 2019.

Vancouver:

Hofmanová M. Degenerate parabolic stochastic partial differential equations : Équations aux dérivées partielles stochastiques paraboliques dégénérées. [Internet] [Doctoral dissertation]. Cachan, Ecole normale supérieure; Charles University. Faculty of mathematics and physics. Department of metal physics (Prague); 2013. [cited 2019 Jun 16]. Available from: http://www.theses.fr/2013DENS0024.

Council of Science Editors:

Hofmanová M. Degenerate parabolic stochastic partial differential equations : Équations aux dérivées partielles stochastiques paraboliques dégénérées. [Doctoral Dissertation]. Cachan, Ecole normale supérieure; Charles University. Faculty of mathematics and physics. Department of metal physics (Prague); 2013. Available from: http://www.theses.fr/2013DENS0024

Western Kentucky University

30. 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)

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 · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th 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 (16^th Edition):

Cheng, Gang. “Analyzing and Solving Non-Linear Stochastic Dynamic Models on Non-Periodic Discrete Time Domains.” 2013. Masters Thesis, Western Kentucky University. Accessed June 16, 2019. https://digitalcommons.wku.edu/theses/1236.

MLA Handbook (7^th Edition):

Cheng, Gang. “Analyzing and Solving Non-Linear Stochastic Dynamic Models on Non-Periodic Discrete Time Domains.” 2013. Web. 16 Jun 2019.

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 2019 Jun 16]. 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

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Open Access Theses and Dissertations