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Introduction to Stochastic Integration K.L. Chung

Introduction to Stochastic Integration By K.L. Chung

Introduction to Stochastic Integration by K.L. Chung


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Summary

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.

Introduction to Stochastic Integration Summary

Introduction to Stochastic Integration by K.L. Chung

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 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 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

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

Introduction to Stochastic Integration Reviews

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 K.L. Chung

Professor Chung and Professor Williams

Table of Contents

1 Preliminaries.- 2 Definition of the Stochastic Integral.- 3 Extension of the Predictable Integrands.- 4 Quadratic Variation Process.- 5 The Ito Formula.- 6 Applications of the Ito Formula.- 7 Local Time and Tanaka's Formula.- 8 Reflected Brownian Motions.- 9 Generalization Ito Formula, Change of Time and Measure.- 10 Stochastic Differential Equations.- References.- Index.

Additional information

NLS9781461495864
9781461495864
1461495865
Introduction to Stochastic Integration by K.L. Chung
New
Paperback
Birkhauser Boston Inc
2013-11-10
276
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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