Brownian Motion and Stochastic Calculus

This book is designed as a text for graduate courses in shastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore shastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of shastic integration and shastic calculus is developed. The power ...