Diffusions, Markov Processes and Martingales. Volume 1, Foundations, 2nd Edition

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L-C-G Rogers et David Williams - .
Now available in paperback, this celebrated book has been prepared with readers' needs in mind, giving a systematic treatment of the subject whilst retaining... Lire la suite
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Résumé

Now available in paperback, this celebrated book has been prepared with readers' needs in mind, giving a systematic treatment of the subject whilst retaining its vitality. The authors' aim is not o present the subject of Brownian motion 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 the theory of stochastic processes. Chapter III is a lively and readable treatment of the theory of Markov processes. Together with Volume 2: Itô Calculus, 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. Cambridge University Press has a long and honourable history of publishing in mathematics and counts many classics of the mathematical literature within its list. Some of these titles have been out of print for many years now and yet the methods which they espouse are still of considerable relevance today. The Cambridge Mathematical Library will provide an inexpensive edition of these titles in a durable paperback format and at a price which will make the books attractive to individuals wishing to add them to their personal libraries. It is intended that certain volumes in the series will have forewords, written by leading experts in the subject, which will place the title in its historical and mathematical context.

Sommaire

  • BROWNIAN MOTION
    • Basics about Brownian motion
    • Brownian motion in higher dimensions
    • Gaussian processes and Lévy processes
  • SOME CLASSICAL THEORY
    • Basic measure theory
    • Basic probability theory
    • Stochastic processes
    • Discrete-parameter Martingale theory
    • Continuous-parameter supermartingales
    • Probability measures on Lusin spaces
  • MARKOV PROCESSES
    • Transition functions and resolvents
    • Feller-dynkin processes
    • Additive functionals
    • Approach to ray processes: the Martin boundary
    • Ray processes
    • Applications.

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