Stopping times and directed processes
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Bibliographic Information
Stopping times and directed processes
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 47）
Cambridge University Press, 2010
- : pbk
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Note
"First published 1992. This digitally printed version 2010" -- T.p. verso
Includes bibliographical references (p. [407]-417) and indexes
Description and Table of Contents
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.
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.
by "Nielsen BookData"