Diffusions, Markov Processes, and Martingales
Diffusions, Markov Processes, and Martingales
Volume 1: Foundations
2nd Edition
May 2000
1. Foundations
Paperback
9780521775946
$89.99
USDPaperback
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.
- Classic book, first time in paperback
- Intuitive and rigorous so suited for graduate students and non-experts
- Comprehensive and up-to-date
Product details
May 2000Paperback
9780521775946
410 pages
229 × 154 × 21 mm
0.56kg
49 exercises
Available
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.
