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Diffusions, Markov Processes, and Martingales

Diffusions, Markov Processes, and Martingales

Volume 1. Foundations

2nd Edition


Part of Cambridge Mathematical Library

  • Date Published: April 2000
  • availability: Available
  • format: Paperback
  • isbn: 9780521775946

£ 65.99

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About the Authors
  • 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.

    • Classic book, first time in paperback
    • Intuitive and rigorous so suited for graduate students and non-experts
    • Comprehensive and up-to-date
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    Product details

    • Edition: 2nd Edition
    • Date Published: April 2000
    • format: Paperback
    • isbn: 9780521775946
    • length: 410 pages
    • dimensions: 229 x 154 x 21 mm
    • weight: 0.56kg
    • contains: 49 exercises
    • availability: 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

  • Authors

    L. C. G. Rogers, University of Bath

    David Williams, University of Wales, Swansea

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