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Stopping Times and Directed Processes

Stopping Times and Directed Processes


Part of Encyclopedia of Mathematics and its Applications

  • Date Published: April 2010
  • availability: Available
  • format: Paperback
  • isbn: 9780521135085
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About the Authors
  • The notion of 'stopping times' is a useful one in probability theory; it can be applied to both classical problems and fresh ones. This book presents this technique in the context of the directed set, stochastic processes indexed by directed sets, and many applications in probability, analysis and ergodic theory. Martingales and related processes are considered from several points of view. The book opens with a discussion of pointwise and stochastic convergence of processes, with concise proofs arising from the method of stochastic convergence. Later, the rewording of Vitali covering conditions in terms of stopping times clarifies connections with the theory of stochastic processes. Solutions are presented here for nearly all the open problems in the Krickeberg convergence theory for martingales and submartingales indexed by directed set. Another theme of the book is the unification of martingale and ergodic theorems.

    • A unified treatment of multiparameter martingale and ergodic theory
    • Martingale and ergodic theories are HOT topics
    • Applies the theory to classical mathematical problems as well as fresh ones
    • Encyclopedic coverage
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    Customer reviews

    31st Jul 2014 by Mrchen

    The book opens with a discussion of pointwise and stochastic convergence of processes with concise proofs arising from the method of stochastic convergence

    Review was not posted due to profanity


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    Product details

    • Date Published: April 2010
    • format: Paperback
    • isbn: 9780521135085
    • length: 444 pages
    • dimensions: 234 x 156 x 23 mm
    • weight: 0.62kg
    • availability: Available
  • Table of Contents

    1. Stopping times
    2. Infinite measure and Orlicz spaces
    3. Inequalities
    4. Directed index set
    5. Banach-valued random variables
    6. Martingales
    7. Derivation
    8. Pointwise ergodic theorems
    9. Multiparameter processes

  • Authors

    G. A. Edgar, Ohio State University

    Louis Sucheston, Ohio State University

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