Probability Theory

Independence, Interchangeability, Martingales

  • Yuan Shih Chow
  • Henry Teicher

Part of the Springer Texts in Statistics book series (STS)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Yuan Shih Chow, Henry Teicher
    Pages 1-29
  3. Yuan Shih Chow, Henry Teicher
    Pages 30-53
  4. Yuan Shih Chow, Henry Teicher
    Pages 54-83
  5. Yuan Shih Chow, Henry Teicher
    Pages 84-112
  6. Yuan Shih Chow, Henry Teicher
    Pages 113-164
  7. Yuan Shih Chow, Henry Teicher
    Pages 270-312
  8. Yuan Shih Chow, Henry Teicher
    Pages 313-353
  9. Yuan Shih Chow, Henry Teicher
    Pages 354-403
  10. Yuan Shih Chow, Henry Teicher
    Pages 404-443
  11. Yuan Shih Chow, Henry Teicher
    Pages 444-477
  12. Back Matter
    Pages 479-489

About this book

Introduction

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.

Keywords

Conditional probability Maxima Probability space Probability theory Random variable Uniform integrability measure theory

Authors and affiliations

  • Yuan Shih Chow
    • 1
  • Henry Teicher
    • 2
  1. 1.Department of StatisticsColumbia UniversityNew YorkUSA
  2. 2.Department of StatisticsRutgers UniversityNew BrunswickUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1950-7
  • Copyright Information Springer-Verlag New York, Inc. 1997
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-40607-7
  • Online ISBN 978-1-4612-1950-7
  • Series Print ISSN 1431-875X
  • About this book