Stopping Time Techniques for Analysts and Probabilists

Stopping Time Techniques for Analysts and Probabilists

by L. Egghe
     
 

ISBN-10: 0521317150

ISBN-13: 9780521317153

Pub. Date: 12/28/2002

Publisher: Cambridge University Press

This book considers convergence of adapted sequences of real and Banach space-valued integrable functions, emphasizing the use of stopping time techniques. Not only are highly specialized results given, but also elementary applications of these results. The book starts by discussing the convergence theory of martingales and sub-( or super-) martingales with values

Overview

This book considers convergence of adapted sequences of real and Banach space-valued integrable functions, emphasizing the use of stopping time techniques. Not only are highly specialized results given, but also elementary applications of these results. The book starts by discussing the convergence theory of martingales and sub-( or super-) martingales with values in a Banach space with or without the Radon-Nikodym property. Several inequalities which are of use in the study of the convergence of more general adapted sequence such as (uniform) amarts, mils and pramarts are proved and sub- and superpramarts are discussed and applied to the convergence of pramarts. Most of the results have a strong relationship with (or in fact are characterizations of) topological or geometrical properties of Banach spaces. The book will interest research and graduate students in probability theory, functional analysis and measure theory, as well as proving a useful textbook for specialized courses on martingale theory.

Product Details

ISBN-13:
9780521317153
Publisher:
Cambridge University Press
Publication date:
12/28/2002
Series:
London Mathematical Society Lecture Note Series, #100
Pages:
368
Product dimensions:
5.98(w) x 8.98(h) x 0.83(d)

Related Subjects

Table of Contents

Preface; 1. Types of convergence; 2. Martingale convergence theorems; 3. Sub- and supermartingale convergence theorems; 4. Basic inequalities for adapted sequences; 5. Convergence of generalized martingales in Banach spaces - the mean way; 6. General directed index sets and applications of amart theory; 7. Disadvantages of amarts: convergence of generalized martingales in Banach spaces - the pointwise way; 8. Convergence of generalized sub- and supermartingales in Banach lattices; 9. Closing remarks; References; List of notations; Subject index.

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