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-xviii
  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 113-158
  7. Yuan Shih Chow, Henry Teicher
    Pages 252-294
  8. Yuan Shih Chow, Henry Teicher
    Pages 295-335
  9. Yuan Shih Chow, Henry Teicher
    Pages 336-385
  10. Yuan Shih Chow, Henry Teicher
    Pages 386-423
  11. Yuan Shih Chow, Henry Teicher
    Pages 424-457
  12. Back Matter
    Pages 458-467

About this book

Introduction

Apart from new examples and exercises, some simplifications of proofs, minor improvements, and correction of typographical errors, the principal change from the first edition is the addition of section 9.5, dealing with the central limit theorem for martingales and more general stochastic arrays. vii Preface to the First Edition Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world. The origins of the sub­ ject, generally attributed to investigations by the renowned French mathe­ matician Fermat of problems posed by a gambling contemporary to Pascal, have been pushed back a century earlier to the Italian mathematicians Cardano and Tartaglia about 1570 (Ore, 1953). Results as significant as the Bernoulli weak law of large numbers appeared as early as 1713, although its counterpart, the Borel strong law oflarge numbers, did not emerge until 1909. Central limit theorems and conditional probabilities were already being investigated in the eighteenth century, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes (1921), von Mises (1928; 1931), and Kolmogorov (1933).

Keywords

Martingal Martingale Maxima Probability theory Random variable conditional probability law of the iterated logarithm measure theory probability space product measure random walk renewal theory uniform integrability

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-0504-0
  • Copyright Information Springer-Verlag New York 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-0506-4
  • Online ISBN 978-1-4684-0504-0
  • Series Print ISSN 1431-875X
  • About this book