In recent years, the study of the theory of Brownian motion has become a powerful tool in the solution of problems in mathematical physics. This self-contained and readable exposition by leading authors, provides a rigorous account of the subject, emphasizing the "explicit" rather than the "concise" where necessary, and addressed to readers interested in probability theory as applied to analysis and mathematical physics.
A distinctive feature of the methods used is the ubiquitous appearance of stopping time. The book contains much original research by the authors (some of which published here for the first time) as well as detailed and improved versions of relevant important results by other authors, not easily accessible in existing literature.

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 Ito 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 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.

"The text also proves that stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has become one of the most powerful tools in modern probability theory. "

Journal of the American Statistical Association

" horizontal dagger separator] "

"An attractive text written in a] lean and precise style eminently readable. Especially pleasant are the care and attention devoted to details A very fine book. "

Mathematical Reviews"

In recent years, the study of the theory of Brownian motion has become a powerful tool in the solution of problems in mathematical physics. This self-contained and readable exposition by leading authors, provides a rigorous account of the subject, emphasizing the "explicit" rather than the "concise" where necessary, and addressed to readers interested in probability theory as applied to analysis and mathematical physics.
A distinctive feature of the methods used is the ubiquitous appearance of stopping time. The book contains much original research by the authors (some of which published here for the first time) as well as detailed and improved versions of relevant important results by other authors, not easily accessible in existing literature.

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 Ito 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 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.

"The text also proves that stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has become one of the most powerful tools in modern probability theory. "

Journal of the American Statistical Association

" horizontal dagger separator] "

"An attractive text written in a] lean and precise style eminently readable. Especially pleasant are the care and attention devoted to details A very fine book. "

Mathematical Reviews