Introduction to Stochastic Integration (Paperback)

K.L. Chung

ISBN 10: 1461495865 / ISBN 13: 9781461495864

Published by Birkhauser Boston Inc, Secaucus, 2013

Paperback. 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 Its change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the FeynmanKac functional and the Schroedinger 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 CameronMartinGirsanov transformation and a final chapter which provides an introduction to stochastic differential equations, as well as many exercises for classroom use.This book willbe 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 An attractive textwritten in [a] lean and precise styleeminently readable. Especially pleasant are the care and attention devoted to details A very fine book.Mathematical Reviews This highly readable introduction to stochastic integration and stochastic differential equations combines developments of the basic theory with applications. It is a softcover reprint of a classic, graduate-level textbook. Includes exercises. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9781461495864

Synopsis:

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 It’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 Schrödinger 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 willbe 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

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

About the Author: Professor Chung and Professor Williams

Bibliographic Details

Title: Introduction to Stochastic Integration (...
Publisher: Birkhauser Boston Inc, Secaucus
Publication Date: 2013
Binding: Paperback
Condition: new
Edition: 2nd Edition