The author, a lucid mind with a fine pedagogical instinct, has written a splendid text. He starts out by stating six problems in the introduction in which stochastic differential equations play an essential role in the solution. Then, while developing stochastic calculus, he frequently returns to these problems and variants thereof and to many other problems to show how the theory works and to motivate the next step in the theoretical development. Needless to say, he restricts himself to stochastic integration with respect to Brownian motion. He is not hesitant to give some basic results without proof in order to leave room for "some more basic applications..." The book can be an ideal text for a graduate course, but it is also recommended to analysts (in particular, those working in differential equations and deterministic dynamical systems and control) who wish to learn quickly what stochastic differential equations are all about.

TABLE OF CONTENTS

I Introduction
II Some Mathematical Preliminaries
III Ito Integrals
IV Ito Processes and the Ito Formula
V Stochastic Differential Equations
VI The Filtering Problem
VII Diffusions: Basic Properties
VIII Other Topics in Diffusion Theory
IX Applications to Boundary Value Problems
X Application to Optimal Stopping
XI Application to Stochastic Control
Appendix A: Normal Random Variables
Appendix B: Conditional Expectations
Appendix C: Uniform Integrability and Martingale Convergence
Solutions and additional hints to some of the exercises
Bibliography
List of Frequently Used Notation and Symbols
Index