Stopping time techniques for analysts and probabilists

L. Egghe

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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[目次]

  • 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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この本の情報

書名 Stopping time techniques for analysts and probabilists
著作者等 Egghe, L.
Hitchin N.J.
Egghe Leo
シリーズ名 London Mathematical Society lecture note series
出版元 Cambridge University Press
刊行年月 1984
ページ数 xvi, 351 p.
大きさ 23 cm
ISBN 0521317150
NCID BA00570068
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言語 英語
出版国 イギリス
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