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  1. Home
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  3. Stopping Times and Directed Processes
  • Cited by 80
Publisher:
Cambridge University Press
Online publication date:
January 2010
Print publication year:
1992
Online ISBN:
9780511574740
DOI:
https://doi.org/10.1017/CBO9780511574740
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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