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.
|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|
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