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- Product code: 20159
- ISBN: 0521775949,
ISBN13: 9780521775946,
406 pages, paperback
Published by Cambridge University Press on 2000
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Description of Diffusions, Markov Processes, and Martingales: Volume 1 |
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.
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Contents of Diffusions, Markov Processes, and Martingales: Volume 1 |
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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