subject:(Martingales)

Michigan State University

1. Boros, Nicholas. The L[superscript p]-operator norm of a quadratic perturbation of the real part of the Ahlfors-Beurling operator.

Degree: 2012, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:459

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Thesis Ph. D. Michigan State University. Mathematics 2012.

Given a sequence of martingale differences, Burkholder found the sharp constant for the Lp-norm of the corresponding… (more)

Subjects/Keywords: Martingales (Mathematics); Mathematics

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

APA (6^th Edition):

Boros, N. (2012). The L[superscript p]-operator norm of a quadratic perturbation of the real part of the Ahlfors-Beurling operator. (Thesis). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:459

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):

Boros, Nicholas. “The L[superscript p]-operator norm of a quadratic perturbation of the real part of the Ahlfors-Beurling operator.” 2012. Thesis, Michigan State University. Accessed March 09, 2021. http://etd.lib.msu.edu/islandora/object/etd:459.

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

MLA Handbook (7^th Edition):

Boros, Nicholas. “The L[superscript p]-operator norm of a quadratic perturbation of the real part of the Ahlfors-Beurling operator.” 2012. Web. 09 Mar 2021.

Vancouver:

Boros N. The L[superscript p]-operator norm of a quadratic perturbation of the real part of the Ahlfors-Beurling operator. [Internet] [Thesis]. Michigan State University; 2012. [cited 2021 Mar 09]. Available from: http://etd.lib.msu.edu/islandora/object/etd:459.

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

Council of Science Editors:

Boros N. The L[superscript p]-operator norm of a quadratic perturbation of the real part of the Ahlfors-Beurling operator. [Thesis]. Michigan State University; 2012. Available from: http://etd.lib.msu.edu/islandora/object/etd:459

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

Washington State University

2. [No author]. A Modified Chang-Wilson-Wolff Inequality Via the Bellman Function .

Degree: 2019, Washington State University

URL: http://hdl.handle.net/2376/16730

► We produce the optimal constant in an inequality bounding the exponential integral of a function by the exponential integral of its dyadic square function. This… (more)

Subjects/Keywords: Mathematics; Bellman; Harmonic Analysis; Martingales

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APA (6^th Edition):

author], [. (2019). A Modified Chang-Wilson-Wolff Inequality Via the Bellman Function . (Thesis). Washington State University. Retrieved from http://hdl.handle.net/2376/16730

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. “A Modified Chang-Wilson-Wolff Inequality Via the Bellman Function .” 2019. Thesis, Washington State University. Accessed March 09, 2021. http://hdl.handle.net/2376/16730.

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. “A Modified Chang-Wilson-Wolff Inequality Via the Bellman Function .” 2019. Web. 09 Mar 2021.

Vancouver:

author] [. A Modified Chang-Wilson-Wolff Inequality Via the Bellman Function . [Internet] [Thesis]. Washington State University; 2019. [cited 2021 Mar 09]. Available from: http://hdl.handle.net/2376/16730.

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

Council of Science Editors:

author] [. A Modified Chang-Wilson-Wolff Inequality Via the Bellman Function . [Thesis]. Washington State University; 2019. Available from: http://hdl.handle.net/2376/16730

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

Columbia University

3. Stebegg, Florian. Linear Constraints in Optimal Transport.

Degree: 2019, Columbia University

URL: https://doi.org/10.7916/d8-k4vs-tb63

► This thesis studies the problem of optimal mass transportation with linear constraints – supermartingale and martingale transport in discrete and continuous time. Appropriate versions of… (more)

Subjects/Keywords: Statistics; Mathematics; Martingales (Mathematics)

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

APA (6^th Edition):

Stebegg, F. (2019). Linear Constraints in Optimal Transport. (Doctoral Dissertation). Columbia University. Retrieved from https://doi.org/10.7916/d8-k4vs-tb63

Chicago Manual of Style (16^th Edition):

Stebegg, Florian. “Linear Constraints in Optimal Transport.” 2019. Doctoral Dissertation, Columbia University. Accessed March 09, 2021. https://doi.org/10.7916/d8-k4vs-tb63.

MLA Handbook (7^th Edition):

Stebegg, Florian. “Linear Constraints in Optimal Transport.” 2019. Web. 09 Mar 2021.

Vancouver:

Stebegg F. Linear Constraints in Optimal Transport. [Internet] [Doctoral dissertation]. Columbia University; 2019. [cited 2021 Mar 09]. Available from: https://doi.org/10.7916/d8-k4vs-tb63.

Council of Science Editors:

Stebegg F. Linear Constraints in Optimal Transport. [Doctoral Dissertation]. Columbia University; 2019. Available from: https://doi.org/10.7916/d8-k4vs-tb63

The Ohio State University

4. Bagchi, Sitadri Nath. On almost sure convergence of classes of multivalued asymptotic martingales.

Degree: PhD, Graduate School, 1983, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1487245320874794

Subjects/Keywords: Mathematics; Martingales

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APA (6^th Edition):

Bagchi, S. N. (1983). On almost sure convergence of classes of multivalued asymptotic martingales. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1487245320874794

Chicago Manual of Style (16^th Edition):

Bagchi, Sitadri Nath. “On almost sure convergence of classes of multivalued asymptotic martingales.” 1983. Doctoral Dissertation, The Ohio State University. Accessed March 09, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487245320874794.

MLA Handbook (7^th Edition):

Bagchi, Sitadri Nath. “On almost sure convergence of classes of multivalued asymptotic martingales.” 1983. Web. 09 Mar 2021.

Vancouver:

Bagchi SN. On almost sure convergence of classes of multivalued asymptotic martingales. [Internet] [Doctoral dissertation]. The Ohio State University; 1983. [cited 2021 Mar 09]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1487245320874794.

Council of Science Editors:

Bagchi SN. On almost sure convergence of classes of multivalued asymptotic martingales. [Doctoral Dissertation]. The Ohio State University; 1983. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1487245320874794

Columbia University

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

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 March 09, 2021. 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. 09 Mar 2021.

Vancouver:

Dandapani A. Enlargement of Filtration and the Strict Local Martingale Property in Stochastic Differential Equations. [Internet] [Doctoral dissertation]. Columbia University; 2016. [cited 2021 Mar 09]. 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

6. Harter, Jonathan. Martingales sur les variétés de valeur terminale donnée : Martingales in manifolds with prescribed terminal value.

Degree: Docteur es, Mathématiques Pures, 2018, Bordeaux

URL: http://www.theses.fr/2018BORD0074

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Définies il y a quelques décennies, les martingales dans les variétés sont maintenant des objets bien connus. Des questions très simples restent en suspens cependant.… (more)

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Définies il y a quelques décennies, les martingales dans les variétés sont maintenant des objets bien connus. Des questions très simples restent en suspens cependant. Par exemple,étant donnée une variable aléatoire à valeurs dans une variété complète, et une filtration continue(dont toute martingale réelle possède une version continue), existe-t-il une martingale continue dans cette variété qui a pour valeur terminale donnée cette variable aléatoire ? Que dire des semimartingales de valeur terminale et dérives données ? Le but principal de cette thèse est d’apporter des réponses à ces questions. Sous des hypothèses de géométrie convexe, des réponses sont données dans les articles de Kendall (1990), Picard (1991), Picard (1994), Darling (1995) ou encore Arnaudon (1997). Le cas des semimartingales a plus largement été traité par Blache (2004). Les martingales dans les variétés permettent de définir les barycentres associés à une filtration, qui sont parfois plus simples à calculer que les barycentres usuels ou les moyennes, et qui possèdent une propriété d’associativité. Ils sont fortement reliés à la théorie du contrôle, à l’optimisation stochastique, ainsi qu’aux équations différentielles stochastiques rétrogrades (EDSRs). La résolution du problème avec des arguments géométriques donne par ailleurs des outils pour résoudre des EDSRs quadratiques multidimensionnelles.Au cours de cette thèse deux principales méthodes ont été employées pour étudier le problème de l’existence de martingale de valeur terminale donnée. La première est basée sur un algorithme stochastique. La variable aléatoire que l’on cherchera à atteindre sera d’abord déformée en une famille ξ(a) de classe C¹, et on se posera la question suivante : existe-t-il une martingale X(a) de valeur terminale ξ(a) ? Une méthode de tir, selon un principe similaire au tir géodésique déterministe, sera employée relativement au paramètre a en direction de la variable aléatoire ξ(a). La seconde est basée sur la résolution générale d’une EDSR multidimensionnelle à croissance quadratique. La principale problématique de cette partie sera d’adapter au cadre multidimensionnel une stratégie récente développée par Briand et Elie (2013) permettant de traiter les EDSRs quadratiques multidimensionnelles. Cette approche nouvelle permet de retrouver la plupart des résultats partiels obtenus par des méthodes différentes. Au-delà de l’intérêt unifiant,cette nouvelle approche ouvre la voie à de potentiels futurs travaux.

Defined several decades ago, martingales in manifolds are very canonical objects. About these objects very simple questions are still unresolved. For instance, given a random variable with values in a complete manifold and a continuous filtration (one with respect to which all real-valued martingales admit a continuous version), does there exist a continuous martingale in the manifold with terminal value given by this random variable ? What about semimartingales with prescribed drift and terminal value ? The main aim of this thesis is to provide answers to these…

Advisors/Committee Members: Arnaudon, Marc (thesis director).

Subjects/Keywords: Martingales; Variétés; Calcul stochastique; EDSRs; EDSRs quadratiques; Martingales; Manifolds; Stochastic calculus; BSDEs; Quadratic BSDEs

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

APA (6^th Edition):

Harter, J. (2018). Martingales sur les variétés de valeur terminale donnée : Martingales in manifolds with prescribed terminal value. (Doctoral Dissertation). Bordeaux. Retrieved from http://www.theses.fr/2018BORD0074

Chicago Manual of Style (16^th Edition):

Harter, Jonathan. “Martingales sur les variétés de valeur terminale donnée : Martingales in manifolds with prescribed terminal value.” 2018. Doctoral Dissertation, Bordeaux. Accessed March 09, 2021. http://www.theses.fr/2018BORD0074.

MLA Handbook (7^th Edition):

Harter, Jonathan. “Martingales sur les variétés de valeur terminale donnée : Martingales in manifolds with prescribed terminal value.” 2018. Web. 09 Mar 2021.

Vancouver:

Harter J. Martingales sur les variétés de valeur terminale donnée : Martingales in manifolds with prescribed terminal value. [Internet] [Doctoral dissertation]. Bordeaux; 2018. [cited 2021 Mar 09]. Available from: http://www.theses.fr/2018BORD0074.

Council of Science Editors:

Harter J. Martingales sur les variétés de valeur terminale donnée : Martingales in manifolds with prescribed terminal value. [Doctoral Dissertation]. Bordeaux; 2018. Available from: http://www.theses.fr/2018BORD0074

Universidade do Rio Grande do Sul

7. Misturini, Ricardo. Movimento browniano, integral de Itô e introdução às equações diferenciais estocásticas.

Degree: 2010, Universidade do Rio Grande do Sul

URL: http://hdl.handle.net/10183/24926

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Este texto apresenta alguns dos elementos básicos envolvidos em um estudo introdutório das equações diferencias estocásticas. Tais equações modelam problemas a tempo contínuo em que… (more)

Subjects/Keywords: Equações diferenciais estocásticas; Brownian motion; Martingales; Martingales; Movimento browniano; Stochastic integral; Itô's Formula; Stochastic differential equations

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

APA (6^th Edition):

Misturini, R. (2010). Movimento browniano, integral de Itô e introdução às equações diferenciais estocásticas. (Thesis). Universidade do Rio Grande do Sul. Retrieved from http://hdl.handle.net/10183/24926

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):

Misturini, Ricardo. “Movimento browniano, integral de Itô e introdução às equações diferenciais estocásticas.” 2010. Thesis, Universidade do Rio Grande do Sul. Accessed March 09, 2021. http://hdl.handle.net/10183/24926.

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

MLA Handbook (7^th Edition):

Misturini, Ricardo. “Movimento browniano, integral de Itô e introdução às equações diferenciais estocásticas.” 2010. Web. 09 Mar 2021.

Vancouver:

Misturini R. Movimento browniano, integral de Itô e introdução às equações diferenciais estocásticas. [Internet] [Thesis]. Universidade do Rio Grande do Sul; 2010. [cited 2021 Mar 09]. Available from: http://hdl.handle.net/10183/24926.

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

Council of Science Editors:

Misturini R. Movimento browniano, integral de Itô e introdução às equações diferenciais estocásticas. [Thesis]. Universidade do Rio Grande do Sul; 2010. Available from: http://hdl.handle.net/10183/24926

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

Université de Bordeaux I

8. Fraysse, Philippe. Estimation récursive dans certains modèles de déformation : Recursive estimation for some deformation models.

Degree: Docteur es, Mathématiques appliquées, 2013, Université de Bordeaux I

URL: http://www.theses.fr/2013BOR14797

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Cette thèse est consacrée à l'étude de certains modèles de déformation semi-paramétriques. Notre objectif est de proposer des méthodes récursives, issues d'algorithmes stochastiques, pour estimer… (more)

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Cette thèse est consacrée à l'étude de certains modèles de déformation semi-paramétriques. Notre objectif est de proposer des méthodes récursives, issues d'algorithmes stochastiques, pour estimer les paramètres de ces modèles. Dans la première partie, on présente les outils théoriques existants qui nous seront utiles dans la deuxième partie. Dans un premier temps, on présente un panorama général sur les méthodes d'approximation stochastique, en se focalisant en particulier sur les algorithmes de Robbins-Monro et de Kiefer-Wolfowitz. Dans un second temps, on présente les méthodes à noyaux pour l'estimation de fonction de densité ou de régression. On s'intéresse plus particulièrement aux deux estimateurs à noyaux les plus courants qui sont l'estimateur de Parzen-Rosenblatt et l'estimateur de Nadaraya-Watson, en présentant les versions récursives de ces deux estimateurs.Dans la seconde partie, on présente tout d'abord une procédure d'estimation récursive semi-paramétrique du paramètre de translation et de la fonction de régression pour le modèle de translation dans la situation où la fonction de lien est périodique. On généralise ensuite ces techniques au modèle vectoriel de déformation à forme commune en estimant les paramètres de moyenne, de translation et d'échelle, ainsi que la fonction de régression. On s'intéresse finalement au modèle de déformation paramétrique de variables aléatoires dans le cadre où la déformation est connue à un paramètre réel près. Pour ces trois modèles, on établit la convergence presque sûre ainsi que la normalité asymptotique des estimateurs paramétriques et non paramétriques proposés. Enfin, on illustre numériquement le comportement de nos estimateurs sur des données simulées et des données réelles.

This thesis is devoted to the study of some semi-parametric deformation models.Our aim is to provide recursive methods, related to stochastic algorithms, in order to estimate the different parameters of the models. In the first part, we present the theoretical tools which we will use in the next part. On the one hand, we focus on stochastic approximation methods, in particular the Robbins-Monro algorithm and the Kiefer-Wolfowitz algorithm. On the other hand, we introduce kernel estimators in order to estimate a probability density function and a regression function. More particularly, we present the two most famous kernel estimators which are the one of Parzen-Rosenblatt and the one of Nadaraya-Watson. We also present their recursive version.In the second part, we present the results we obtained in this thesis.Firstly, we provide a recursive estimation method of the shift parameter and the regression function for the translation model in which the regression function is periodic. Secondly, we extend this estimation procedure to the shape invariant model, providing estimation of the height parameter, the translation parameter and the scale parameter, as well as the common shape function.Thirdly, we are interested in the parametric deformation model of random variables where the deformation…

Advisors/Committee Members: Bercu, Bernard (thesis director).

Subjects/Keywords: Estimation récursive; Modèles semi-paramétriques; Algorithmes stochastiques; Estimateurs à noyaux; Martingales; Recursive estimation; Semi-parametric models; Stochastic algorithms; Kernel estimators; Martingales

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

APA (6^th Edition):

Fraysse, P. (2013). Estimation récursive dans certains modèles de déformation : Recursive estimation for some deformation models. (Doctoral Dissertation). Université de Bordeaux I. Retrieved from http://www.theses.fr/2013BOR14797

Chicago Manual of Style (16^th Edition):

Fraysse, Philippe. “Estimation récursive dans certains modèles de déformation : Recursive estimation for some deformation models.” 2013. Doctoral Dissertation, Université de Bordeaux I. Accessed March 09, 2021. http://www.theses.fr/2013BOR14797.

MLA Handbook (7^th Edition):

Fraysse, Philippe. “Estimation récursive dans certains modèles de déformation : Recursive estimation for some deformation models.” 2013. Web. 09 Mar 2021.

Vancouver:

Fraysse P. Estimation récursive dans certains modèles de déformation : Recursive estimation for some deformation models. [Internet] [Doctoral dissertation]. Université de Bordeaux I; 2013. [cited 2021 Mar 09]. Available from: http://www.theses.fr/2013BOR14797.

Council of Science Editors:

Fraysse P. Estimation récursive dans certains modèles de déformation : Recursive estimation for some deformation models. [Doctoral Dissertation]. Université de Bordeaux I; 2013. Available from: http://www.theses.fr/2013BOR14797

University of Alberta

9. Tsoi, Allanus Hak-Man. Integration by parts and time reversal.

Degree: PhD, Department of Statistics and Applied Probability, 1990, University of Alberta

URL: https://era.library.ualberta.ca/files/qb98mh204

Subjects/Keywords: Stochastic processes.; Martingales (Mathematics)

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

APA (6^th Edition):

Tsoi, A. H. (1990). Integration by parts and time reversal. (Doctoral Dissertation). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/qb98mh204

Chicago Manual of Style (16^th Edition):

Tsoi, Allanus Hak-Man. “Integration by parts and time reversal.” 1990. Doctoral Dissertation, University of Alberta. Accessed March 09, 2021. https://era.library.ualberta.ca/files/qb98mh204.

MLA Handbook (7^th Edition):

Tsoi, Allanus Hak-Man. “Integration by parts and time reversal.” 1990. Web. 09 Mar 2021.

Vancouver:

Tsoi AH. Integration by parts and time reversal. [Internet] [Doctoral dissertation]. University of Alberta; 1990. [cited 2021 Mar 09]. Available from: https://era.library.ualberta.ca/files/qb98mh204.

Council of Science Editors:

Tsoi AH. Integration by parts and time reversal. [Doctoral Dissertation]. University of Alberta; 1990. Available from: https://era.library.ualberta.ca/files/qb98mh204

Penn State University

10. Pardo, John Jacob. Randomness of Restricted Value Martingales, Selection Rules, and Graph Sequences.

Degree: 2017, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/13948jjp307

► In this dissertation we consider the classical notions of stochasticity and randomness as they pertain to several areas of mathematics. We look at three main… (more)

▼ In this dissertation we consider the classical notions of stochasticity and randomness as they pertain to several areas of mathematics. We look at three main topics: martingales, selection rules, and graphs. First, we discuss the notion of martingales and focus our attention onto restricted value martingales; this allows us to make some insights into the notion of A-valued randomness for a set A of real numbers. Martingales are the classical mathematical representation of a betting strategy; they are defined in a way that nicely accommodates the notion of ``win your bet if you are successful and lose your bet if you are unsuccessful.'' By looking at restricted value martingales, we are able to focus on betting strategies that only allow wagers of certain amounts. Bavly and Peretz defined notions of anticipation and evasion to relate the relative strengths of restricted value martingales; this provides a natural way to compare A-valued randomness and B-valued randomness for different sets A, B \subseteq \R⁺. Essentially, A evades B when there is an A-martingale that can succeed against any countable set of B-martingales, and otherwise B anticipates A – to get the similar notion of single evasion one only needs to consider a single B-martingale. Bavly and Peretz characterized the evasion/anticipation relationships when A is bounded and B is bounded away from 0, as well as when B is well-ordered, however the question of what happens when B has 0 as an accumulation point remained open. We look at various geometric sequences for our set B to help answer this question with regard to single evasion/single anticipation. Second, we consider selection rules and how they relate to normality and randomness. Traditionally, a selection rule indicates how to select a subsequence from a given binary sequence based on the initial segment of the sequence that has already been viewed. Clearly one must ask what sort of properties are preserved under the application of a selection rule, however there are two equally important ways to formulate this question: for a fixed set of sequences what selection rules always output an element of that set when applied to an element of that set, and for a fixed set of selection rules what properties of sequences are preserved? Von Mises made the intuitions of these questions rigorous with the notions of kollektivs and admissible selection rules. We focus on sequences and selection rules defined in terms of computability, normality, Martin-Löf randomness, and the strong law of large numbers. Lastly, we apply selection rules to graphs and graph sequences as well as discuss several notions of randomness for graphs. Graphs as mathematical objects are intuitively more structurally complicated than binary sequences, however both graphs and sequences are useful to consider in the context of information content. As a result, it makes sense to look at any probabilistic notion that applies to binary sequences – stochasticity, normality, randomness – … Advisors/Committee Members: Jan Reimann, Dissertation Advisor/Co-Advisor, Jan Reimann, Committee Chair/Co-Chair, Stephen Simpson, Committee Member, Manfred Denker, Committee Member, Martin Furer, Outside Member.

Subjects/Keywords: Randomness; Selection Rules; Restricted Value Martingales; Normality; Graphs

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

APA (6^th Edition):

Pardo, J. J. (2017). Randomness of Restricted Value Martingales, Selection Rules, and Graph Sequences. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/13948jjp307

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):

Pardo, John Jacob. “Randomness of Restricted Value Martingales, Selection Rules, and Graph Sequences.” 2017. Thesis, Penn State University. Accessed March 09, 2021. https://submit-etda.libraries.psu.edu/catalog/13948jjp307.

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

MLA Handbook (7^th Edition):

Pardo, John Jacob. “Randomness of Restricted Value Martingales, Selection Rules, and Graph Sequences.” 2017. Web. 09 Mar 2021.

Vancouver:

Pardo JJ. Randomness of Restricted Value Martingales, Selection Rules, and Graph Sequences. [Internet] [Thesis]. Penn State University; 2017. [cited 2021 Mar 09]. Available from: https://submit-etda.libraries.psu.edu/catalog/13948jjp307.

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

Council of Science Editors:

Pardo JJ. Randomness of Restricted Value Martingales, Selection Rules, and Graph Sequences. [Thesis]. Penn State University; 2017. Available from: https://submit-etda.libraries.psu.edu/catalog/13948jjp307

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

Stellenbosch University

11. Tchamga, Nicole Flaure Kouemo. Portfolio optimization problems : a martingale and a convex duality approach.

Degree: Mathematical Sciences, 2010, Stellenbosch University

URL: http://hdl.handle.net/10019.1/5259

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Thesis (MSc (Mathematics)) – University of Stellenbosch, 2010.

ENGLISH ABSTRACT: The first approach initiated by Merton [Mer69, Mer71] to solve utility maximization portfolio problems in continuous… (more)

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Thesis (MSc (Mathematics)) – University of Stellenbosch, 2010.

ENGLISH ABSTRACT: The first approach initiated by Merton [Mer69, Mer71] to solve utility maximization portfolio problems in continuous time is based on stochastic control theory. The idea of Merton was to interpret the maximization portfolio problem as a stochastic control problem where the trading strategies are considered as a control process and the portfolio wealth as the controlled process. Merton derived the Hamilton-Jacobi-Bellman (HJB) equation and for the special case of power, logarithm and exponential utility functions he produced a closedform solution. A principal disadvantage of this approach is the requirement of the Markov property for the stocks prices. The so-called martingale method represents the second approach for solving utility maximization portfolio problems in continuous time. It was introduced by Pliska [Pli86], Cox and Huang [CH89, CH91] and Karatzas et al. [KLS87] in di erent variant. It is constructed upon convex duality arguments and allows one to transform the initial dynamic portfolio optimization problem into a static one and to resolve it without requiring any \Markov" assumption. A de nitive answer (necessary and su cient conditions) to the utility maximization portfolio problem for terminal wealth has been obtained by Kramkov and Schachermayer [KS99]. In this thesis, we study the convex duality approach to the expected utility maximization problem (from terminal wealth) in continuous time stochastic markets, which as already mentioned above can be traced back to the seminal work by Merton [Mer69, Mer71]. Before we detail the structure of our thesis, we would like to emphasize that the starting point of our work is based on Chapter 7 in Pham [P09] a recent textbook. However, as the careful reader will notice, we have deepened and added important notions and results (such as the study of the upper (lower) hedge, the characterization of the essential supremum of all the possible prices, compare Theorem 7.2.2 in Pham [P09] with our stated Theorem 2.4.9, the dynamic programming equation 2.31, the superhedging theorem 2.6.1...) and we have made a considerable e ort in the proofs. Indeed, several proofs of theorems in Pham [P09] have serious gaps (not to mention typos) and even aws (for example see the proof of Proposition 7.3.2 in Pham [P09] and our proof of Proposition 3.4.8). In the rst chapter, we state the expected utility maximization problem and motivate the convex dual approach following an illustrative example by Rogers [KR07, R03]. We also brie y review the von Neumann - Morgenstern Expected Utility Theory. In the second chapter, we begin by formulating the superreplication problem as introduced by El Karoui and Quenez [KQ95]. The fundamental result in the literature on super-hedging is the dual characterization of the set of all initial endowments leading to a super-hedge of a European contingent claim. El Karoui and Quenez [KQ95] rst proved the superhedging theorem 2.6.1 in…

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

Subjects/Keywords: Mathematics; Martingales (Mathematics); Optimal investment

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APA (6^th Edition):

Tchamga, N. F. K. (2010). Portfolio optimization problems : a martingale and a convex duality approach. (Thesis). Stellenbosch University. Retrieved from http://hdl.handle.net/10019.1/5259

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):

Tchamga, Nicole Flaure Kouemo. “Portfolio optimization problems : a martingale and a convex duality approach.” 2010. Thesis, Stellenbosch University. Accessed March 09, 2021. http://hdl.handle.net/10019.1/5259.

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

MLA Handbook (7^th Edition):

Tchamga, Nicole Flaure Kouemo. “Portfolio optimization problems : a martingale and a convex duality approach.” 2010. Web. 09 Mar 2021.

Vancouver:

Tchamga NFK. Portfolio optimization problems : a martingale and a convex duality approach. [Internet] [Thesis]. Stellenbosch University; 2010. [cited 2021 Mar 09]. Available from: http://hdl.handle.net/10019.1/5259.

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

Council of Science Editors:

Tchamga NFK. Portfolio optimization problems : a martingale and a convex duality approach. [Thesis]. Stellenbosch University; 2010. Available from: http://hdl.handle.net/10019.1/5259

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

University of Otago

12. Monk, Travis. The Evolutionary Origin of Nervous Systems and Implications for Neural Computation .

Degree: 2014, University of Otago

URL: http://hdl.handle.net/10523/4804

► If neurones are the answer, then what was the question? Nervous systems are remarkably conserved throughout the animal kingdom. This conservation indicates that their core… (more)

▼ If neurones are the answer, then what was the question? Nervous systems are remarkably conserved throughout the animal kingdom. This conservation indicates that their core design and function features were established very early in their evolutionary history. It also indicates that all nervous systems solve the same fundamental task in essentially the same way, and have been doing so since their inception. Understanding when and why animals evolved nervous systems could help us identify that fundamental task. It could also provide context to help us determine how nervous systems solve that task so well. This thesis studies the evolutionary origins of nervous systems and the ecological conditions under which they evolved. It outlines fossil, ecological, and molecular evidence to argue that animals evolved nervous systems soon after they started eating each other, 550 million years ago. When animals started eating each other, they must have experienced a selection pressure to react to threats and opportunities in a precisely-timed manner. Nervous systems could have been one response to this selection pressure. This thesis then provides a quantitative ecological argument that, before animals started eating each other, they were forbidden from evolving neurones, but after, they were forced to either evolve neurones or be driven to extinction by a competitor that did. If predation was the question, then why are neurones the answer? This thesis argues that the first afferent sensory neurones were threshold detectors that produced spikes to alert animals of the proximity of other animals. Those spikes prompted a reaction, such as striking or fleeing, the instant that a state of the world became critical. Ancient animals would have found utility in devices that signalled as soon as the probability that a world state was critical exceeded some threshold. Extant neurones are well-adapted to solve these tasks; they produce an all-or-nothing spike when their membrane potential exceeds a threshold. Given that their core function features have hardly changed since their inception, they may still be functioning in an analogous manner. When animals evolved devices that spiked conditional on world states, it became possible for them to infer those states, given the spiking output of the devices. This thesis shows this principle explicitly with idealised models of predator-prey interactions. If an animal could implement Bayesian inference given sensory spikes, then that animal would extract all possible information about the world from those spikes; no ‘neural coding’ strategy can contain more information about the world. In situations requiring fast decision-making and reaction in accordance with potentially-fatal states of the world, an animal that uses Bayes’ rule to make inferences about the world from sensory spikes would outperform all competitors. Extant nervous systems could implement Bayesian inference by functioning as a biological analogue of a particle filter. Advisors/Committee Members: Paulin, Michael G (advisor).

Subjects/Keywords: Bayesian neurons; Predation; Evolution of Nervous Systems; Origin of Neurons; Martingales

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APA (6^th Edition):

Monk, T. (2014). The Evolutionary Origin of Nervous Systems and Implications for Neural Computation . (Doctoral Dissertation). University of Otago. Retrieved from http://hdl.handle.net/10523/4804

Chicago Manual of Style (16^th Edition):

Monk, Travis. “The Evolutionary Origin of Nervous Systems and Implications for Neural Computation .” 2014. Doctoral Dissertation, University of Otago. Accessed March 09, 2021. http://hdl.handle.net/10523/4804.

MLA Handbook (7^th Edition):

Monk, Travis. “The Evolutionary Origin of Nervous Systems and Implications for Neural Computation .” 2014. Web. 09 Mar 2021.

Vancouver:

Monk T. The Evolutionary Origin of Nervous Systems and Implications for Neural Computation . [Internet] [Doctoral dissertation]. University of Otago; 2014. [cited 2021 Mar 09]. Available from: http://hdl.handle.net/10523/4804.

Council of Science Editors:

Monk T. The Evolutionary Origin of Nervous Systems and Implications for Neural Computation . [Doctoral Dissertation]. University of Otago; 2014. Available from: http://hdl.handle.net/10523/4804

University of Colorado

13. Chakarov, Aleksandar Nevenov. Deductive Verification of Infinite-State Stochastic Systems Using Martingales.

Degree: PhD, Computer Science, 2016, University of Colorado

URL: https://scholar.colorado.edu/csci_gradetds/130

► The focus of this dissertation is the analysis of and verification of discrete time stochastic systems using martingales. Martingale theory yields a powerful set… (more)

Subjects/Keywords: Formal Methdos; Martingales; Stochastic Systems; Verification; Computer Sciences

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APA (6^th Edition):

Chakarov, A. N. (2016). Deductive Verification of Infinite-State Stochastic Systems Using Martingales. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/csci_gradetds/130

Chicago Manual of Style (16^th Edition):

Chakarov, Aleksandar Nevenov. “Deductive Verification of Infinite-State Stochastic Systems Using Martingales.” 2016. Doctoral Dissertation, University of Colorado. Accessed March 09, 2021. https://scholar.colorado.edu/csci_gradetds/130.

MLA Handbook (7^th Edition):

Chakarov, Aleksandar Nevenov. “Deductive Verification of Infinite-State Stochastic Systems Using Martingales.” 2016. Web. 09 Mar 2021.

Vancouver:

Chakarov AN. Deductive Verification of Infinite-State Stochastic Systems Using Martingales. [Internet] [Doctoral dissertation]. University of Colorado; 2016. [cited 2021 Mar 09]. Available from: https://scholar.colorado.edu/csci_gradetds/130.

Council of Science Editors:

Chakarov AN. Deductive Verification of Infinite-State Stochastic Systems Using Martingales. [Doctoral Dissertation]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/csci_gradetds/130

Columbia University

14. Qiu, Lisha. Stochastic Differential Equations and Strict Local Martingales.

Degree: 2018, Columbia University

URL: https://doi.org/10.7916/D8F4911Q

► In this thesis, we address two problems arising from the application of stochastic differential equations (SDEs). The first one pertains to the detection of asset… (more)

▼ In this thesis, we address two problems arising from the application of stochastic differential equations (SDEs). The first one pertains to the detection of asset bubbles, where the price process solves an SDE. We combine the strict local martingale model together with a statistical tool to instantaneously check the existence and severity of asset bubbles through the asset’s historical price process. Our approach assumes that the price process of interest is a CEV process. We relate the exponent parameter in the CEV process to an asset bubble by studying the future expectation and the running maximum of the CEV process. The detection of asset bubbles then boils down to the estimation of the exponent. With a dynamic linear regression model, inference on the exponent can be carried out using historical price data. Estimation of the volatility and calibration of the parameters in the dynamic linear regression model are also studied. When using SDEs in practice, for example, in the detection of asset bubbles, one often would like to simulate its paths using the Euler scheme to study the behavior of the solution. The second part of this thesis focuses on the convergence property of the Euler scheme under the assumption that the coefficients of the SDE are locally Lipschitz and that the solution has no finite explosion. We prove that if a numerical scheme converges uniformly on any compact time set (UCP) in probability with a certain rate under the globally Lipschitz condition, then when the globally Lipschitz condition is replaced with a locally Lipschitz one plus a no finite explosion condition, UCP convergence with the same rate holds. One contribution of this thesis is the proof of √n-weak convergence of the asymptotic normalized error process. The limit error process is also provided. We further study the boundedness for the second moment of the weak limit process and its running maximum under both the globally Lipschitz and the locally Lipschitz conditions. The convergence of the Euler scheme in the sense of approximating expectations of functionals is also studied under the locally Lipschitz condition

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

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APA (6^th Edition):

Qiu, L. (2018). Stochastic Differential Equations and Strict Local Martingales. (Doctoral Dissertation). Columbia University. Retrieved from https://doi.org/10.7916/D8F4911Q

Chicago Manual of Style (16^th Edition):

Qiu, Lisha. “Stochastic Differential Equations and Strict Local Martingales.” 2018. Doctoral Dissertation, Columbia University. Accessed March 09, 2021. https://doi.org/10.7916/D8F4911Q.

MLA Handbook (7^th Edition):

Qiu, Lisha. “Stochastic Differential Equations and Strict Local Martingales.” 2018. Web. 09 Mar 2021.

Vancouver:

Qiu L. Stochastic Differential Equations and Strict Local Martingales. [Internet] [Doctoral dissertation]. Columbia University; 2018. [cited 2021 Mar 09]. Available from: https://doi.org/10.7916/D8F4911Q.

Council of Science Editors:

Qiu L. Stochastic Differential Equations and Strict Local Martingales. [Doctoral Dissertation]. Columbia University; 2018. Available from: https://doi.org/10.7916/D8F4911Q

Hong Kong University of Science and Technology

15. Kong, Xin-Bing. Statistical inferences on jumps of semi-martingales using high frequency data.

Degree: 2011, Hong Kong University of Science and Technology

URL: http://repository.ust.hk/ir/Record/1783.1-61817 ; https://doi.org/10.14711/thesis-b1146139 ; http://repository.ust.hk/ir/bitstream/1783.1-61817/1/th_redirect.html

► In this thesis, I study the following two problems by using discretely observed high frequency data. • How active are jumps in the underlying continuous-time… (more)

▼ In this thesis, I study the following two problems by using discretely observed high frequency data. • How active are jumps in the underlying continuous-time dynamic which are modeled by semi-martingales? • Could we model the underlying continuous-time dynamic by a pure jump process? The thesis consists of three parts. First, under a general semi-martingale process, I propose a new estimator of the jump activity index (JAI hereafter) which is a natural measure of the relative occurring frequency of jumps defined by Ait-Sahalia and Jacod (2009b). Since small jumps were properly included in the estimator, the newly proposed estimator is more efficient than the one given in Ait-Sahalia and Jacod (2009b). Theoretically, the new estimator is proved to be consistent and a central limit theorem is obtained. Simulation studies justifies the good performance of the new estimator. A real example is also presented. Second, the effect of the microstructure noise on estimation of JAI is investigated. It turns out that the existence of the microstructure noise leads to a significant bias on estimation of JAI. A two-step procedure is proposed to give a consistent estimator of the JAI under noisy observations. In the first step, a local smoothing technique is used to eliminate the effect of the microstructure noise and a modified noise-cleaned data set is obtained. In the second step, based on the noise-cleaned data set, several estimators are presented under three different model settings, Models I-III with increasing generality. Consistency of the estimators is proved under all models. Asymptotic normality is shown for the estimators under Model I and Model II. Simulations and the real data analysis shows that the estimator under Model I is robust to the presence of microstructure noise and performs reasonably well. Third, to answer whether the underlying dynamic is a pure-jump semi-martingale or not, a test is developed. The test is very simple to use and yet effective. Asymptotic properties of the test statistic are studied. Simulations show that the test could control the type I error probabilities no matter how actively the jumps occur, and that the test is very powerful. Three real data sets are analyzed and all data sets support the pure-jump modeling of the underlying dynamics.

Subjects/Keywords: Estimation theory ; Mathematical models ; Jump processes ; Martingales (Mathematics)

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APA (6^th Edition):

Kong, X. (2011). Statistical inferences on jumps of semi-martingales using high frequency data. (Thesis). Hong Kong University of Science and Technology. Retrieved from http://repository.ust.hk/ir/Record/1783.1-61817 ; https://doi.org/10.14711/thesis-b1146139 ; http://repository.ust.hk/ir/bitstream/1783.1-61817/1/th_redirect.html

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):

Kong, Xin-Bing. “Statistical inferences on jumps of semi-martingales using high frequency data.” 2011. Thesis, Hong Kong University of Science and Technology. Accessed March 09, 2021. http://repository.ust.hk/ir/Record/1783.1-61817 ; https://doi.org/10.14711/thesis-b1146139 ; http://repository.ust.hk/ir/bitstream/1783.1-61817/1/th_redirect.html.

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

MLA Handbook (7^th Edition):

Kong, Xin-Bing. “Statistical inferences on jumps of semi-martingales using high frequency data.” 2011. Web. 09 Mar 2021.

Vancouver:

Kong X. Statistical inferences on jumps of semi-martingales using high frequency data. [Internet] [Thesis]. Hong Kong University of Science and Technology; 2011. [cited 2021 Mar 09]. Available from: http://repository.ust.hk/ir/Record/1783.1-61817 ; https://doi.org/10.14711/thesis-b1146139 ; http://repository.ust.hk/ir/bitstream/1783.1-61817/1/th_redirect.html.

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

Council of Science Editors:

Kong X. Statistical inferences on jumps of semi-martingales using high frequency data. [Thesis]. Hong Kong University of Science and Technology; 2011. Available from: http://repository.ust.hk/ir/Record/1783.1-61817 ; https://doi.org/10.14711/thesis-b1146139 ; http://repository.ust.hk/ir/bitstream/1783.1-61817/1/th_redirect.html

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

Michigan State University

16. Chari, Ravi. Weak convergence of distribution-valued semimartingales and associated SDE's.

Degree: PhD, Department of Statistics and Probability, 1984, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:34216

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

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APA (6^th Edition):

Chari, R. (1984). Weak convergence of distribution-valued semimartingales and associated SDE's. (Doctoral Dissertation). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:34216

Chicago Manual of Style (16^th Edition):

Chari, Ravi. “Weak convergence of distribution-valued semimartingales and associated SDE's.” 1984. Doctoral Dissertation, Michigan State University. Accessed March 09, 2021. http://etd.lib.msu.edu/islandora/object/etd:34216.

MLA Handbook (7^th Edition):

Chari, Ravi. “Weak convergence of distribution-valued semimartingales and associated SDE's.” 1984. Web. 09 Mar 2021.

Vancouver:

Chari R. Weak convergence of distribution-valued semimartingales and associated SDE's. [Internet] [Doctoral dissertation]. Michigan State University; 1984. [cited 2021 Mar 09]. Available from: http://etd.lib.msu.edu/islandora/object/etd:34216.

Council of Science Editors:

Chari R. Weak convergence of distribution-valued semimartingales and associated SDE's. [Doctoral Dissertation]. Michigan State University; 1984. Available from: http://etd.lib.msu.edu/islandora/object/etd:34216

17. Spring, William Joseph. A quantum stochastic calculus.

Degree: PhD, 2012, University of Hertfordshire

URL: http://hdl.handle.net/2299/9240

► Martingales are fundamental stochastic process used to model the concept of fair game. They have a multitude of applications in the real world that include,… (more)

Subjects/Keywords: 519.2; quantum; processes; stochastic; multiparameter; martingales; adapted processes

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APA (6^th Edition):

Spring, W. J. (2012). A quantum stochastic calculus. (Doctoral Dissertation). University of Hertfordshire. Retrieved from http://hdl.handle.net/2299/9240

Chicago Manual of Style (16^th Edition):

Spring, William Joseph. “A quantum stochastic calculus.” 2012. Doctoral Dissertation, University of Hertfordshire. Accessed March 09, 2021. http://hdl.handle.net/2299/9240.

MLA Handbook (7^th Edition):

Spring, William Joseph. “A quantum stochastic calculus.” 2012. Web. 09 Mar 2021.

Vancouver:

Spring WJ. A quantum stochastic calculus. [Internet] [Doctoral dissertation]. University of Hertfordshire; 2012. [cited 2021 Mar 09]. Available from: http://hdl.handle.net/2299/9240.

Council of Science Editors:

Spring WJ. A quantum stochastic calculus. [Doctoral Dissertation]. University of Hertfordshire; 2012. Available from: http://hdl.handle.net/2299/9240

Louisiana State University

18. Sae-Tang, Anuwat. A new theory of stochastic integration.

Degree: PhD, Applied Mathematics, 2011, Louisiana State University

URL: etd-07052011-203013 ; https://digitalcommons.lsu.edu/gradschool_dissertations/893

► In this dissertation, we focus mainly on the further study of the new stochastic integral introduced by Ayed and Kuo in 2008. Several properties of… (more)

Subjects/Keywords: new stochastic integrals; Ayed-Kuo integrals; near-martingales

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APA (6^th Edition):

Sae-Tang, A. (2011). A new theory of stochastic integration. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-07052011-203013 ; https://digitalcommons.lsu.edu/gradschool_dissertations/893

Chicago Manual of Style (16^th Edition):

Sae-Tang, Anuwat. “A new theory of stochastic integration.” 2011. Doctoral Dissertation, Louisiana State University. Accessed March 09, 2021. etd-07052011-203013 ; https://digitalcommons.lsu.edu/gradschool_dissertations/893.

MLA Handbook (7^th Edition):

Sae-Tang, Anuwat. “A new theory of stochastic integration.” 2011. Web. 09 Mar 2021.

Vancouver:

Sae-Tang A. A new theory of stochastic integration. [Internet] [Doctoral dissertation]. Louisiana State University; 2011. [cited 2021 Mar 09]. Available from: etd-07052011-203013 ; https://digitalcommons.lsu.edu/gradschool_dissertations/893.

Council of Science Editors:

Sae-Tang A. A new theory of stochastic integration. [Doctoral Dissertation]. Louisiana State University; 2011. Available from: etd-07052011-203013 ; https://digitalcommons.lsu.edu/gradschool_dissertations/893

University of Texas – Austin

19. Haynes, Alan Kaan. Tools and techniques in diophantine approximation.

Degree: PhD, Mathematics, 2006, University of Texas – Austin

URL: http://hdl.handle.net/2152/2717

Subjects/Keywords: Diophantine approximation; Martingales (Mathematics)

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APA (6^th Edition):

Haynes, A. K. (2006). Tools and techniques in diophantine approximation. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/2717

Chicago Manual of Style (16^th Edition):

Haynes, Alan Kaan. “Tools and techniques in diophantine approximation.” 2006. Doctoral Dissertation, University of Texas – Austin. Accessed March 09, 2021. http://hdl.handle.net/2152/2717.

MLA Handbook (7^th Edition):

Haynes, Alan Kaan. “Tools and techniques in diophantine approximation.” 2006. Web. 09 Mar 2021.

Vancouver:

Haynes AK. Tools and techniques in diophantine approximation. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2006. [cited 2021 Mar 09]. Available from: http://hdl.handle.net/2152/2717.

Council of Science Editors:

Haynes AK. Tools and techniques in diophantine approximation. [Doctoral Dissertation]. University of Texas – Austin; 2006. Available from: http://hdl.handle.net/2152/2717

Purdue University

20. Perlmutter, Michael A. Martingales, Singular Integrals, and Fourier Multipliers.

Degree: PhD, Mathematics, 2016, Purdue University

URL: https://docs.lib.purdue.edu/open_access_dissertations/829

► Many probabilistic constructions have been created to study the Lp-boundedness, 1 < p < ∞, of singular integrals and Fourier multipliers. We will use… (more)

Subjects/Keywords: Pure sciences; Beurling-ahlfors; Harmonic analysis; Martingales; Probability; Singular integrals; Mathematics

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APA (6^th Edition):

Perlmutter, M. A. (2016). Martingales, Singular Integrals, and Fourier Multipliers. (Doctoral Dissertation). Purdue University. Retrieved from https://docs.lib.purdue.edu/open_access_dissertations/829

Chicago Manual of Style (16^th Edition):

Perlmutter, Michael A. “Martingales, Singular Integrals, and Fourier Multipliers.” 2016. Doctoral Dissertation, Purdue University. Accessed March 09, 2021. https://docs.lib.purdue.edu/open_access_dissertations/829.

MLA Handbook (7^th Edition):

Perlmutter, Michael A. “Martingales, Singular Integrals, and Fourier Multipliers.” 2016. Web. 09 Mar 2021.

Vancouver:

Perlmutter MA. Martingales, Singular Integrals, and Fourier Multipliers. [Internet] [Doctoral dissertation]. Purdue University; 2016. [cited 2021 Mar 09]. Available from: https://docs.lib.purdue.edu/open_access_dissertations/829.

Council of Science Editors:

Perlmutter MA. Martingales, Singular Integrals, and Fourier Multipliers. [Doctoral Dissertation]. Purdue University; 2016. Available from: https://docs.lib.purdue.edu/open_access_dissertations/829

The Ohio State University

21. Frangos, Nicholas E. On convergence and regularity of vector-valued processes indexed by directed sets.

Degree: PhD, Graduate School, 1984, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1487257452614184

Subjects/Keywords: Mathematics; Martingales; Set theory

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APA (6^th Edition):

Frangos, N. E. (1984). On convergence and regularity of vector-valued processes indexed by directed sets. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1487257452614184

Chicago Manual of Style (16^th Edition):

Frangos, Nicholas E. “On convergence and regularity of vector-valued processes indexed by directed sets.” 1984. Doctoral Dissertation, The Ohio State University. Accessed March 09, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487257452614184.

MLA Handbook (7^th Edition):

Frangos, Nicholas E. “On convergence and regularity of vector-valued processes indexed by directed sets.” 1984. Web. 09 Mar 2021.

Vancouver:

Frangos NE. On convergence and regularity of vector-valued processes indexed by directed sets. [Internet] [Doctoral dissertation]. The Ohio State University; 1984. [cited 2021 Mar 09]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1487257452614184.

Council of Science Editors:

Frangos NE. On convergence and regularity of vector-valued processes indexed by directed sets. [Doctoral Dissertation]. The Ohio State University; 1984. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1487257452614184

Rhodes University

22. Glover, Elistan Nicholas. Analytic pricing of American put options.

Degree: Faculty of Science, Statistics, 2009, Rhodes University

URL: http://hdl.handle.net/10962/d1002804

► American options are the most commonly traded financial derivatives in the market. Pricing these options fairly, so as to avoid arbitrage, is of paramount importance.… (more)

Subjects/Keywords: Options (Finance) – Prices – Mathematical models; Derivative securities – Prices – Mathematical models; Finance – Mathematical models; Martingales (Mathematics)

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APA (6^th Edition):

Glover, E. N. (2009). Analytic pricing of American put options. (Thesis). Rhodes University. Retrieved from http://hdl.handle.net/10962/d1002804

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):

Glover, Elistan Nicholas. “Analytic pricing of American put options.” 2009. Thesis, Rhodes University. Accessed March 09, 2021. http://hdl.handle.net/10962/d1002804.

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

MLA Handbook (7^th Edition):

Glover, Elistan Nicholas. “Analytic pricing of American put options.” 2009. Web. 09 Mar 2021.

Vancouver:

Glover EN. Analytic pricing of American put options. [Internet] [Thesis]. Rhodes University; 2009. [cited 2021 Mar 09]. Available from: http://hdl.handle.net/10962/d1002804.

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

Council of Science Editors:

Glover EN. Analytic pricing of American put options. [Thesis]. Rhodes University; 2009. Available from: http://hdl.handle.net/10962/d1002804

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

University of Adelaide

23. Roughan, Matthew. An application of martingales to queueing theory / Matthew Roughan.

Degree: 1993, University of Adelaide

URL: http://hdl.handle.net/2440/21478

Subjects/Keywords: 519.82 20; Martingales (Mathematics); Queuing theory.

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

APA (6^th Edition):

Roughan, M. (1993). An application of martingales to queueing theory / Matthew Roughan. (Thesis). University of Adelaide. Retrieved from http://hdl.handle.net/2440/21478

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):

Roughan, Matthew. “An application of martingales to queueing theory / Matthew Roughan.” 1993. Thesis, University of Adelaide. Accessed March 09, 2021. http://hdl.handle.net/2440/21478.

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

MLA Handbook (7^th Edition):

Roughan, Matthew. “An application of martingales to queueing theory / Matthew Roughan.” 1993. Web. 09 Mar 2021.

Vancouver:

Roughan M. An application of martingales to queueing theory / Matthew Roughan. [Internet] [Thesis]. University of Adelaide; 1993. [cited 2021 Mar 09]. Available from: http://hdl.handle.net/2440/21478.

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

Council of Science Editors:

Roughan M. An application of martingales to queueing theory / Matthew Roughan. [Thesis]. University of Adelaide; 1993. Available from: http://hdl.handle.net/2440/21478

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

Michigan State University

24. Hannig, Jan. On purely discontinuous martingales.

Degree: PhD, Department of Statistics and Probability, 2000, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:28367

Subjects/Keywords: Martingales (Mathematics); Stochastic processes; Filters (Mathematics)

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

APA (6^th Edition):

Hannig, J. (2000). On purely discontinuous martingales. (Doctoral Dissertation). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:28367

Chicago Manual of Style (16^th Edition):

Hannig, Jan. “On purely discontinuous martingales.” 2000. Doctoral Dissertation, Michigan State University. Accessed March 09, 2021. http://etd.lib.msu.edu/islandora/object/etd:28367.

MLA Handbook (7^th Edition):

Hannig, Jan. “On purely discontinuous martingales.” 2000. Web. 09 Mar 2021.

Vancouver:

Hannig J. On purely discontinuous martingales. [Internet] [Doctoral dissertation]. Michigan State University; 2000. [cited 2021 Mar 09]. Available from: http://etd.lib.msu.edu/islandora/object/etd:28367.

Council of Science Editors:

Hannig J. On purely discontinuous martingales. [Doctoral Dissertation]. Michigan State University; 2000. Available from: http://etd.lib.msu.edu/islandora/object/etd:28367

Vilnius University

25. Dzindzalieta, Dainius. Tiksliosios Bernulio tikimybių nelygybės.

Degree: PhD, Mathematics, 2014, Vilnius University

URL: http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2014~D_20140512_103759-89684 ;

►

Disertacijos darbo tikslas – įrodyti universalias tiksliąsias nelygybes atsitiktinių dydžių funkcijų nukrypimo nuo vidurkio tikimybėms. Universalios nelygybės pažymi, kad jos yra tolygios pagal tam tikras… (more)

▼

Disertacijos darbo tikslas – įrodyti universalias tiksliąsias nelygybes atsitiktinių dydžių funkcijų nukrypimo nuo vidurkio tikimybėms. Universalios nelygybės pažymi, kad jos yra tolygios pagal tam tikras bendras skirstinių klases ir pagal atsitiktinių dydžių kiekį, kartais ir pagal kitus parametrus. Nelygybės vadinamos tiksliosiomis, jeigu pavyksta sukonstruoti atsitiktinių dydžių seką, kuriai nelygybės virsta lygybėmis. Tokios nelygybės labai naudingos, pavyzdžiui, draudimo matematikoje, konstruojant efektyvius algoritmus. Disertaciją sudaro šeši skyriai. Pirmasis skyrius yra įvadas, kuriame neformaliai pristatomas disertacijoje tiriamas objektas, pateikiamas bendras darbo aprašymas ir motyvacija. Detalesnė kitų autorių rezultatų apžvalga pateikiama atskirai kiekviename skyriuje. Antrasis skyrius skirtas atvejui, kai atsitiktiniai dydžiai yra aprėžti ir simetriniai. Trečiajame skyriuje įrodomos nelygybės atsitiktiniams dydžiams, tenkinantiems dispersijos aprėžtumo sąlygą. Ketvirtajame skyriuje nagrinėjamos sąlyginai aprėžtų atsitiktinių dydžių sumos. Penktajame skyriuje tiriamos atsitiktinių dydžių sekos, sudarančios martingalą arba supermartingalą, ir joms gaunamos universaliosios tikimybinės nelygybės ir sukonstruojama nehomogeninė Markovo grandinė, kuri yra martingalas, ir kuriai minėtos nelygybės virsta lygybėmis. Šeštajame skyriuje rezultatai yra apibendrinami atsitiktinių dydžių sekos Lipšico funkcijoms.

The purpose of the dissertation is to prove universal tight bounds for deviation from the mean probability inequalities for functions of random variables. Universal bounds shows that they are uniform with respect to some class of distributions and quantity of variables and other parameters. The bounds are called tight, if we can construct a sequence of random variables, such that the upper bounds are achieved. Such inequalities are useful for example in insurance mathematics, for constructing effective algorithms. We extend the results for Lipschitz functions on general probability metric spaces.

Advisors/Committee Members: KUBILIUS, KĘSTUTIS (Doctoral dissertation committee chair), DUČINSKAS, KĘSTUTIS (Doctoral dissertation committee member), PAULAUSKAS, VYGANTAS (Doctoral dissertation committee member), SURGAILIS, DONATAS (Doctoral dissertation committee member), ŠIAUČIŪNAS, DARIUS (Doctoral dissertation committee member), BIKELIS, ALGIMANTAS JONAS (Doctoral dissertation opponent), RADAVIČIUS, MARIJUS (Doctoral dissertation opponent).

Subjects/Keywords: Nepriklausomi atsitiktiniai dydžiai; Uodegų tikimybės; Lipšico funkcijos; Martingalai; Ekstremali kombinatorika; Random variables; Tail probabilities; Martingales; Lipschitz functions; Extremal combinatorics

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

APA (6^th Edition):

Dzindzalieta, D. (2014). Tiksliosios Bernulio tikimybių nelygybės. (Doctoral Dissertation). Vilnius University. Retrieved from http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2014~D_20140512_103759-89684 ;

Chicago Manual of Style (16^th Edition):

Dzindzalieta, Dainius. “Tiksliosios Bernulio tikimybių nelygybės.” 2014. Doctoral Dissertation, Vilnius University. Accessed March 09, 2021. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2014~D_20140512_103759-89684 ;.

MLA Handbook (7^th Edition):

Dzindzalieta, Dainius. “Tiksliosios Bernulio tikimybių nelygybės.” 2014. Web. 09 Mar 2021.

Vancouver:

Dzindzalieta D. Tiksliosios Bernulio tikimybių nelygybės. [Internet] [Doctoral dissertation]. Vilnius University; 2014. [cited 2021 Mar 09]. Available from: http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2014~D_20140512_103759-89684 ;.

Council of Science Editors:

Dzindzalieta D. Tiksliosios Bernulio tikimybių nelygybės. [Doctoral Dissertation]. Vilnius University; 2014. Available from: http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2014~D_20140512_103759-89684 ;

Vilnius University

26. Dzindzalieta, Dainius. Tight Bernoulli tail probability bounds.

Degree: Dissertation, Mathematics, 2014, Vilnius University

URL: http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2014~D_20140512_103743-38560 ;

►

The purpose of the dissertation is to prove universal tight bounds for deviation from the mean probability inequalities for functions of random variables. Universal bounds… (more)

▼

The purpose of the dissertation is to prove universal tight bounds for deviation from the mean probability inequalities for functions of random variables. Universal bounds shows that they are uniform with respect to some class of distributions and quantity of variables and other parameters. The bounds are called tight, if we can construct a sequence of random variables, such that the upper bounds are achieved. Such inequalities are useful for example in insurance mathematics, for constructing effective algorithms. We extend the results for Lipschitz functions on general probability metric spaces.

Disertacijos darbo tikslas – įrodyti universalias tiksliąsias nelygybes atsitiktinių dydžių funkcijų nukrypimo nuo vidurkio tikimybėms. Universalios nelygybės pažymi, kad jos yra tolygios pagal tam tikras bendras skirstinių klases ir pagal atsitiktinių dydžių kiekį, kartais ir pagal kitus parametrus. Nelygybės vadinamos tiksliosiomis, jeigu pavyksta sukonstruoti atsitiktinių dydžių seką, kuriai nelygybės virsta lygybėmis. Tokios nelygybės labai naudingos, pavyzdžiui, draudimo matematikoje, konstruojant efektyvius algoritmus. Disertaciją sudaro šeši skyriai. Pirmasis skyrius yra įvadas, kuriame neformaliai pristatomas disertacijoje tiriamas objektas, pateikiamas bendras darbo aprašymas ir motyvacija. Detalesnė kitų autorių rezultatų apžvalga pateikiama atskirai kiekviename skyriuje. Antrasis skyrius skirtas atvejui, kai atsitiktiniai dydžiai yra aprėžti ir simetriniai. Trečiajame skyriuje įrodomos nelygybės atsitiktiniams dydžiams, tenkinantiems dispersijos aprėžtumo sąlygą. Ketvirtajame skyriuje nagrinėjamos sąlyginai aprėžtų atsitiktinių dydžių sumos. Penktajame skyriuje tiriamos atsitiktinių dydžių sekos, sudarančios martingalą arba supermartingalą, ir joms gaunamos universaliosios tikimybinės nelygybės ir sukonstruojama nehomogeninė Markovo grandinė, kuri yra martingalas, ir kuriai minėtos nelygybės virsta lygybėmis. Šeštajame skyriuje rezultatai yra apibendrinami atsitiktinių dydžių sekos Lipšico funkcijoms.

Advisors/Committee Members: KUBILIUS, KĘSTUTIS (Doctoral dissertation committee chair), DUČINSKAS, KĘSTUTIS (Doctoral dissertation committee member), PAULAUSKAS, VYGANTAS (Doctoral dissertation committee member), SURGAILIS, DONATAS (Doctoral dissertation committee member), ŠIAUČIŪNAS, DARIUS (Doctoral dissertation committee member), BIKELIS, ALGIMANTAS JONAS (Doctoral dissertation opponent), RADAVIČIUS, MARIJUS (Doctoral dissertation opponent).

Subjects/Keywords: Random variables; Tail probabilities; Martingales; Lipschitz functions; Extremal combinatorics; Nepriklausomi atsitiktiniai dydžiai; Uodegų tikimybės; Lipšico funkcijos; Martingalai; Ekstremali kombinatorika

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

APA (6^th Edition):

Dzindzalieta, D. (2014). Tight Bernoulli tail probability bounds. (Doctoral Dissertation). Vilnius University. Retrieved from http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2014~D_20140512_103743-38560 ;

Chicago Manual of Style (16^th Edition):

Dzindzalieta, Dainius. “Tight Bernoulli tail probability bounds.” 2014. Doctoral Dissertation, Vilnius University. Accessed March 09, 2021. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2014~D_20140512_103743-38560 ;.

MLA Handbook (7^th Edition):

Dzindzalieta, Dainius. “Tight Bernoulli tail probability bounds.” 2014. Web. 09 Mar 2021.

Vancouver:

Dzindzalieta D. Tight Bernoulli tail probability bounds. [Internet] [Doctoral dissertation]. Vilnius University; 2014. [cited 2021 Mar 09]. Available from: http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2014~D_20140512_103743-38560 ;.

Council of Science Editors:

Dzindzalieta D. Tight Bernoulli tail probability bounds. [Doctoral Dissertation]. Vilnius University; 2014. Available from: http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2014~D_20140512_103743-38560 ;

Western Kentucky University

27. Ekiz, Funda. Cagan Type Rational Expectations Model on Time Scales with Their Applications to Economics.

Degree: MS, Department of Mathematics and Computer Science, 2011, Western Kentucky University

URL: https://digitalcommons.wku.edu/theses/1126

► Rational expectations provide people or economic agents making future decision with available information and past experiences. The first approach to the idea of rational… (more)

▼ Rational expectations provide people or economic agents making future decision with available information and past experiences. The first approach to the idea of rational expectations was given approximately fifty years ago by John F. Muth. Many models in economics have been studied using the rational expectations idea. The most familiar one among them is the rational expectations version of the Cagans hyperination model where the expectation for tomorrow is formed using all the information available today. This model was reinterpreted by Thomas J. Sargent and Neil Wallace in 1973. After that time, many solution techniques were suggested to solve the Cagan type rational expectations (CTRE) model. Some economists such as Muth [13], Taylor [26] and Shiller [27] consider the solutions admitting an infinite moving-average representation. Blanchard and Kahn [28] find solutions by using a recursive procedure. A general characterization of the solution was obtained using the martingale approach by Broze, Gourieroux and Szafarz in [22], [23]. We choose to study martingale solution of CTRE model. This thesis is comprised of five chapters where the main aim is to study the CTRE model on isolated time scales. Most of the models studied in economics are continuous or discrete. Discrete models are more preferable by economists since they give more meaningful and accurate results. Discrete models only contain uniform time domains. Time scale calculus enables us to study on m-periodic time domains as well as non periodic time domains. In the first chapter, we give basics of time scales calculus and stochastic calculus. The second chapter is the brief introduction to rational expectations and the CTRE model. Moreover, many other solution techniques are examined in this chapter. After we introduce the necessary background, in the third chapter we construct the CTRE Model on isolated time scales. Then we give the general solution of this model in terms of martingales. We continue our work with defining the linear system and higher order CTRE on isolated time scales. We use Putzer Algorithm to solve the system of the CTRE Model. Then, we examine the existence and uniqueness of the solution of the CTRE model. In the fourth chapter, we apply our solution algorithm developed in the previous chapter to models in Finance and stochastic growth models in Economics. Advisors/Committee Members: Dr. Ferhan Atici (Director), Dr. John Spraker, Dr. Alex Lebedinsky.

Subjects/Keywords: rational expectations; isolated time scale; conditional expectations; martingales; growth models; Discrete Mathematics and Combinatorics; Economic Theory; Mathematics; Statistical Models

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

APA (6^th Edition):

Ekiz, F. (2011). Cagan Type Rational Expectations Model on Time Scales with Their Applications to Economics. (Masters Thesis). Western Kentucky University. Retrieved from https://digitalcommons.wku.edu/theses/1126

Chicago Manual of Style (16^th Edition):

Ekiz, Funda. “Cagan Type Rational Expectations Model on Time Scales with Their Applications to Economics.” 2011. Masters Thesis, Western Kentucky University. Accessed March 09, 2021. https://digitalcommons.wku.edu/theses/1126.

MLA Handbook (7^th Edition):

Ekiz, Funda. “Cagan Type Rational Expectations Model on Time Scales with Their Applications to Economics.” 2011. Web. 09 Mar 2021.

Vancouver:

Ekiz F. Cagan Type Rational Expectations Model on Time Scales with Their Applications to Economics. [Internet] [Masters thesis]. Western Kentucky University; 2011. [cited 2021 Mar 09]. Available from: https://digitalcommons.wku.edu/theses/1126.

Council of Science Editors:

Ekiz F. Cagan Type Rational Expectations Model on Time Scales with Their Applications to Economics. [Masters Thesis]. Western Kentucky University; 2011. Available from: https://digitalcommons.wku.edu/theses/1126

Western Kentucky University

28. 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 March 09, 2021. 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. 09 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 09]. 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

University of Oxford

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

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

Lionnet, Arnaud. “Topics on backward stochastic differential equations : theoretical and practical aspects.” 2013. Doctoral Dissertation, University of Oxford. Accessed March 09, 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 (7^th Edition):

Lionnet, Arnaud. “Topics on backward stochastic differential equations : theoretical and practical aspects.” 2013. Web. 09 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 09]. 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 Edinburgh

30. Bocharov, Boris. Stochastic evolution inclusions.

Degree: PhD, 2010, University of Edinburgh

URL: http://hdl.handle.net/1842/3772

► This work is concerned with an evolution inclusion of a form, in a triple of spaces \V -> H -> V*", where U is a… (more)

Subjects/Keywords: 510; evolution equations; square integrable Lévy martingales.

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

APA (6^th Edition):

Bocharov, B. (2010). Stochastic evolution inclusions. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/3772

Chicago Manual of Style (16^th Edition):

Bocharov, Boris. “Stochastic evolution inclusions.” 2010. Doctoral Dissertation, University of Edinburgh. Accessed March 09, 2021. http://hdl.handle.net/1842/3772.

MLA Handbook (7^th Edition):

Bocharov, Boris. “Stochastic evolution inclusions.” 2010. Web. 09 Mar 2021.

Vancouver:

Bocharov B. Stochastic evolution inclusions. [Internet] [Doctoral dissertation]. University of Edinburgh; 2010. [cited 2021 Mar 09]. Available from: http://hdl.handle.net/1842/3772.

Council of Science Editors:

Bocharov B. Stochastic evolution inclusions. [Doctoral Dissertation]. University of Edinburgh; 2010. Available from: http://hdl.handle.net/1842/3772

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Open Access Theses and Dissertations