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  1. Home
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  3. Stopping Time Techniques for Analysts and Probabilists
  • Cited by 40
Publisher:
Cambridge University Press
Online publication date:
March 2010
Print publication year:
1984
Online ISBN:
9780511526176
DOI:
https://doi.org/10.1017/CBO9780511526176
Subjects:
Mathematics (general), Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
Series:
London Mathematical Society Lecture Note Series (100)
Information

Book description

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.

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