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

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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.
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Editorial Reviews

Booknews
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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Product Details

  • ISBN-13: 9780521775946
  • Publisher: Cambridge University Press
  • Publication date: 4/28/2000
  • Series: Cambridge Mathematical Library Series
  • Edition description: Revised Edition
  • Edition number: 2
  • Pages: 406
  • 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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