A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduate course in stochastic calculus, following a course in probability.

        Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales; then Itô's change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the Feynman-Kac functional and the Schrodinger equation. For Brownian motion, the topics of local time, reflected Brownian motion, and time change are discussed.

        New to the second edition are a discussion of the Cameron-Martin-Girsanov transformation and a final chapter which provides an introduction to stochastic differential equations, as well as many exercises for classroom use.

        This book will be a valuable resource to all mathematicians, statisticians, economists, and engineers employing the modern tools of stochastic analysis.



        Common terms and phrases:
        bounded variation Brownian motion continuous local martingale denote quadratic variation stochastic integral uniformly integrable