Diffusions, Markov Processes, and Martingales: Volume 1, Foundations
Series: Cambridge Mathematical Library;
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Product details:
- Edition number and title Foundations v. 1
- Edition number 2, Revised
- Publisher Cambridge University Press
- Date of Publication 13 April 2000
- ISBN 9780521775946
- Binding Paperback
- No. of pages410 pages
- Size 229x154x21 mm
- Weight 560 g
- Language English
- Illustrations 49 exercises 0
Categories
Short description:
Now available in paperback for the first time; essential reading for all students of probability theory.
MoreLong description:
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.
MoreTable 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 L&&&233;vy 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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