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Stopping Times and Directed Processes by Gerald A. Edgar, Louis Sucheston (1992, Hardcover, Illustrated) 
Stopping Times and Directed Processes by Gerald A. Edgar, Louis Sucheston (1992, Hardcover, Illustrated)

 
Stopping Times and Directed Processes by Gerald A. Edgar, Louis Sucheston (1992, Hardcover, Illustrated)

Author: Gerald A. Edgar, Louis Sucheston
Publisher: Cambridge Univ Pr
Publication Date: 1992-07-01
Series: Encyclopedia of Mathematics and Its Applications
Language: English
Format: Hardcover
ISBN-10: 0521350239
ISBN-13: 9780521350235
Product ID: EPID1102082
Portions of this page Copyright 1995 - 2009 Muze Inc. All rights reserved.
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Details
Publication Date:1992-07-01
Series:Encyclopedia of Mathematics and Its Applications
Edition Description:Illustrated

Size
Length:428 pages
Height:9.8 in
Width:6.5 in
Thickness:1.2 in
Weight:28.8 oz

Publisher's Note
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.

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