Stochastic Analysis

This book is intended for university seniors and graduate students majoring in probability theory or mathematical finance. In the first chapter, results in probability theory are reviewed. Then, it follows a discussion of discrete-time martingales, continuous time square integrable martingales (particularly, continuous martingales of continuous paths), shastic integrations with respect to continuous local martingales, and shastic differential equations driven by Brownian motions. In the fin...