Probability Theory: Independence, Interchangeability, Martingales (Springer Texts in Statistics)

Chow, Yuan Shih; Teicher, Henry

ISBN 10: 0387982280 / ISBN 13: 9780387982281

Published by Springer, 1997

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Bibliographic Details

• Title: Probability Theory: Independence, Interchangeability, Martingales (Springer Texts in Statistics)
• Publisher: Springer
• Publication Date: 1997
• Language: English
• ISBN 10: 0387982280
• ISBN 13: 9780387982281
• Binding: Hardcover
• Edition: 3rd Edition
• Condition: New

About this title

Synopsis

Now available in paperback. This is a text comprising the major theorems of probability theory and the measure theoretical foundations of the subject. The main topics treated are independence, interchangeability,and martingales; particular emphasis is placed upon stopping times, both as tools in proving theorems and as objects of interest themselves. No prior knowledge of measure theory is assumed and a unique feature of the book is the combined presentation of measure and probability. It is easily adapted for graduate students familar with measure theory as indicated by the guidelines in the preface. Special features include: A comprehensive treatment of the law of the iterated logarithm; the Marcinklewicz-Zygmund inequality, its extension to martingales and applications thereof;  development and applications of the second moment analogue of Wald's equation; limit theorems for martingale arrays, the central limit theorem for the interchangeable and martingale cases, moment convergence in the central limit theorem; complete discussion, including central limit theorem, of the random casting of r balls into n cells; recent martingale inequalities; Cram r-L vy theore and factor-closed families of distributions. This edition includes a section dealing with U-statistic, adds additional theorems and examples, and includes simpler versions of some proofs.

Synopsis

This textbook, aimed at graduate students and researchers, comprises the major theorems of probability theory and the measure theoretical foundations of the subject. The main topics treated are independence, interchangeability and martingales, with particular emphasis placed on stopping times, both as tools in providing theorems and as objects of interest themselves. This new edition also contains material on U-statistic, additional theorems and examples and simpler versions of some proofs. No prior knowledge of measure theory is assumed.