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

Now available in paperback for the first time; essential reading for all students of probability theory.

L. C. G. Rogers (Author), David Williams (Author)

9780521775946, Cambridge University Press

Paperback, published 13 April 2000

410 pages, 49 exercises
22.9 x 15.4 x 2.1 cm, 0.56 kg

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.

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.

Subject Areas: Number theory [PBH]