LMS: 100 Stopping Time Techniques (London Mathematical Society Lecture Note Series)
Cambridge University Press, 8/21/2008
EAN 9780521317153, ISBN10: 0521317150
Paperback, 368 pages, 22.9 x 15.2 x 2.3 cm
Language: English
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.
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.