Introduction to Stochastic Integration (Modern Birkhäuser Classics) - Softcover

Chung, K.L. Lai; Williams, R.J.

Softcover

ISBN 10: 1461495865 ISBN 13: 9781461495864

Verlag: Birkhäuser, 2013

Inhaltsangabe

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

Über diesen Titel

Über die Autorin bzw. den Autor

Professor Chung and Professor Williams

Von der hinteren Coverseite

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 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 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

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2013
• Sprache: Englisch
• ISBN 10: 1461495865
• ISBN 13: 9781461495864
• Einband: Tapa blanda
• Auflage: 2
• Anzahl der Seiten: 296
• Kontakt zum Hersteller: Nicht verfügbar