Diffusions, Markov Processes, and Martingales: Volume 1, Foundations

by L. C. G. Rogers, David Williams

Overview

Now available in paperback, this celebrated book has been prepared with readers' needs in mind, remaining a systematic guide to a large part of the modern theory of Probability, whilst retaining its vitality. The authors' aim is to present the subject of Brownian motion not as a dry part of mathematical analysis, but to convey its real meaning and fascination. The opening, heuristic chapter does just this, and it is followed by a comprehensive and self-contained account of the foundations of theory of stochastic processes. Chapter 3 is a lively and readable account of the theory of Markov processes. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.

Product Details

ISBN-13:	9781107713499
Publisher:	Cambridge University Press
Publication date:	04/13/2000
Series:	Cambridge Mathematical Library
Sold by:	Barnes & Noble
Format:	eBook
File size:	21 MB
Note:	This product may take a few minutes to download.

Table of Contents

Some frequently used notation; 1. Brownian motion; Part I. Introduction: 2. Basics about Brownian motion; 3. Brownian motion in higher dimensions; 4. Gaussian processes and Lévy processes; Part II. Some Classical Theory: 5. Basic measure theory; 6. Basic probability theory; 7. Stochastic processes; 8. Discrete-parameter martingale theory; 9. Continuous-parameter martingale theory; 10. Probability measure on Lusin spaces; Part III. Markov Processes: 11. Transition functions and resolvents; 12. Feller–Dynkin processes; 13. Additive functionals; 14. Approach to ray processes: the Martin boundary; 15. Ray processes; 16. Applications; References; Index.

Editorial Reviews

This graduate level textbook deals with Brownian motion, the theory of stochastic processes, and the theory of Markov processes. Topics include Gaussian processes, continuous-parameter supermartingales, probability measure on Lusin spaces, Feller-Dynkin processes, additive functionals, and Ray processes. The second edition extends the coverage of Brownian motion and stochastic processes. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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