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  3. Stopping Times and Directed Processes
  • Cited by 82
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    • Publisher:
      Cambridge University Press
      Publication date:
      January 2010
      August 1992
      ISBN:
      9780511574740
      9780521350235
      9780521135085
      DOI:
      https://doi.org/10.1017/CBO9780511574740
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.819kg, 444 Pages
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.62kg, 444 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
      Series:
      Encyclopedia of Mathematics and its Applications (47)
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
    Series:
    Encyclopedia of Mathematics and its Applications (47)
    Information

    Book description

    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.

    Reviews

    "...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

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