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Probability Theory : Independence, Interchangeability, Martingales - Yuan Shih Chow

Probability Theory

Independence, Interchangeability, Martingales

Hardcover

Published: 11th September 1997
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  • Paperback View Product Published: 17th October 2003
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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.

Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
List of Abbreviations
List of Symbols and Conventions
Classes of Sets, Measures, and Probability Spacesp. 1
Binomial Random Variablesp. 30
Independencep. 54
Integration in a Probability Spacep. 84
Sums of Independent Random Variablesp. 113
Measure Extensions, Lebesgue-Stieltjes Measure, Kolmogorov Consistency Theoremp. 165
Conditional Expectation, Conditional Independence, Introduction to Martingalesp. 210
Distribution Functions and Characteristic Functionsp. 270
Central Limit Theoremsp. 313
Limit Theorems for Independent Random Variablesp. 354
Martingalesp. 404
Infinitely Divisible Lawsp. 444
Indexp. 479
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387982281
ISBN-10: 0387982280
Series: Springer Texts in Statistics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 489
Published: 11th September 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.77 x 16.51  x 3.18
Weight (kg): 0.85
Edition Number: 3
Edition Type: Revised