BASIC THEORIES OF STOCHASTIC DIFFERENTIAL EQUATIONS

Abstract

This project presents basic theory of stochastic differential equations. I start with fundamental stochastic processes such as Brownian motion and the Wiener process, then define Itô's integral and study Itô's formula, the fundamental theorem of stochastic calculus. Next, I present techniques for solving stochastic differential equations and state the Existence and Uniqueness Theorem for these equations. I also discuss the differences between stochastic differential equations and non-stochastic differential equations. Finally, I explore the applications of stochastic differential equations