Stopping Times and Directed Processes Encyclopedia of Mathematics & Its Applications

Edgar, Gerald A., G. A. Edgar and Louis Sucheston:

ISBN 10: 0521350239 / ISBN 13: 9780521350235

Published by Cambridge University Press, 1992

About this Item

428 Seiten Das hier angebotene Buch stammt aus einer teilaufgelösten Bibliothek und kann die entsprechenden Kennzeichnungen aufweisen (Rückenschild, Instituts-Stempel.); der Buchzustand ist ansonsten ordentlich und dem Alter entsprechend gut. Original-Schutzumschlag vorhanden (siehe Foto). In ENGLISCHER Sprache. Sprache: Englisch Gewicht in Gramm: 845.

Seller Inventory # 2218815

Bibliographic Details

• Title: Stopping Times and Directed Processes Encyclopedia of Mathematics & Its Applications
• Publisher: Cambridge University Press
• Publication Date: 1992
• Language: English
• ISBN 10: 0521350239
• ISBN 13: 9780521350235
• Binding: gebundene Ausgabe
• Condition: Gut
• Dust Jacket Condition: Dust Jacket Included
• Weight: 845 grams
• Seller catalogs:
  • 200 Mathematik

About this title

Synopsis

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.

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.