This book provides a comprehensive introduction to the theory of stochastic calculus and some
of its applications. It is the only textbook on the subject to include more than two hundred
exercises with complete solutions. After explaining the basic elements of probability the
author introduces more advanced topics such as Brownian motion martingales and Markov
processes. The core of the book covers stochastic calculus including stochastic differential
equations the relationship to partial differential equations numerical methods and simulation
as well as applications of stochastic processes to finance. The final chapter provides detailed
solutions to all exercises in some cases presenting various solution techniques together with
a discussion of advantages and drawbacks of the methods used. Stochastic Calculus will be
particularly useful to advanced undergraduate and graduate students wishing to acquire a solid
understanding of the subject through the theory and exercises. Including full mathematical
statements and rigorous proofs this book is completely self-contained and suitable for lecture
courses as well as self-study.
