Date of Award

5-1-2018

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Schurz, Henri

Abstract

In this dissertation, we discuss the existence and uniqueness of Ito-type stochastic functional differential equations with infinite memory using fixed point theorem technique. We also address the properties of the solution which are an upper bound for the pth moments of the solution and the Lp-regularity. Then, we provide an analysis to show the local asymptotic L2-stability of the trivial solution using fixed point theorem technique, and we give an approximation of the solution using Euler-Maruyama method providing the global error followed by simulating examples.

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