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

Paperback | May 1, 2000

byL. C. G. Rogers, David Williams

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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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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 fou...

Format:PaperbackDimensions:406 pages, 8.98 × 5.98 × 0.91 inPublished:May 1, 2000Language:English

The following ISBNs are associated with this title:

ISBN - 10:0521775949

ISBN - 13:9780521775946

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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.