Dissertation/Thesis Abstract

Uniqueness Properties in the Theory of Stochastic Differential Equations
by Gomez Henao, Alejandro, Ph.D., University of Rochester, 2013, 56; 3555025
Abstract (Summary)

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 equations using Itô's theory of stochastic calculus allowing to study the usual wave or heat equation, accounting for unknown events that can modify the solutions.

This work contains three major parts. The first part proves uniqueness of the solution to a stochastic differential equation. This equation has relations with the wave equation and is a first attempt to prove uniqueness for a stochastic partial differential equation. The second part focuses on a new method to prove uniqueness for stochastic partial differential equations. This method transforms the question of uniqueness from the stochastic partial differential equation to a doubly backward stochastic differential equation. The third part is the study of an equivalence relation of binary matrices. I develop an algorithm to find the representative of each class of binary matrices.

Indexing (document details)
Advisor: Mueller, Carl
Commitee: Greenleaf, Allan, Shapir, Yonathan
School: University of Rochester
Department: School of Arts and Sciences
School Location: United States -- New York
Source: DAI-B 74/07(E), Dissertation Abstracts International
Subjects: Applied Mathematics, Mathematics
Keywords: Binary matrices, Stochastic differential equations, Stochastic processes, Uniqueness
Publication Number: 3555025
ISBN: 9781267960955
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