Diffusions, Markov Processes, and Martingales: Volume 1, Foundations / Edition 2

by L. C. G. Rogers, David Williams

Overview

Now available in paperback, this celebrated book remains a key systematic guide to a large part of the modern theory of Probability. The authors not only present the subject of Brownian motion as a dry part of mathematical analysis, but 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 presentation of the theory of Markov processes. Together with its companion volume, this book equips graduate students for research into a subject of great intrinsic interest and wide applications.

Product Details

ISBN-13:	9780521775946
Publisher:	Cambridge University Press
Publication date:	04/13/2000
Series:	Cambridge Mathematical Library , #1
Edition description:	Revised Edition
Pages:	410
Product dimensions:	6.06(w) x 9.02(h) x 0.83(d)

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)

Booknews