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

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

by D. Williams, David Williams, L. C. G. Rogers
 

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ISBN-10: 0521775949

ISBN-13: 9780521775946

Pub. Date: 09/28/2014

Publisher: Cambridge University Press

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

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:
09/28/2014
Series:
Cambridge Mathematical Library Series
Edition description:
Revised Edition
Pages:
406
Sales rank:
379,136
Product dimensions:
5.98(w) x 8.98(h) x 0.91(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.

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