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Stopping Times and Directed Processes

Stopping Times and Directed Processes

$61.00 ( ) USD

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: February 2011
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511828690
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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 new ones. This book presents this technique in the context of the directed set, stochastic processes indexed by directed sets, and provides many applications in probability, analysis, and ergodic theory. 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 is the unification of martingale and ergodic theorems. Among the topics treated are: the three-function maximal inequality, Burkholder's martingale transform inequality and prophet inequalities, convergence in Banach spaces, and a general superadditive ration ergodic theorem. From this, the general Chacon-Ornstein theorem and the Chacon theorem can be derived. A second instance of the unity of ergodic and martingale theory is a general principle showing that in both theories, all the multiparameter convergence theorems follow from one-parameter maximal and convergence 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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    Reviews & endorsements

    "...will be extremely valuable to anybody doing research on directed processes. It is highly original. Most of the material has been published only in research journals so far....will be an indispensable and rich source of information previously scattered throughout many journals." U. Krengel, Mathematical Reviews

    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: February 2011
    • format: Adobe eBook Reader
    • isbn: 9780511828690
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Introduction
    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
    References
    Index.

  • Authors

    G. A. Edgar, Ohio State University

    Louis Sucheston, Ohio State University

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