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Probability Theory

Independence, Interchangeability, Martingales

  • Textbook
  • © 1988

Overview

Authors:
  1. Yuan Shih Chow

    1. Department of Mathematical Statistics, Columbia University, New York, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Henry Teicher

    1. Department of Statistics, Rutgers University, New Brunswick, USA

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Classes of Sets, Measures, and Probability Spaces

    • Yuan Shih Chow, Henry Teicher
    Pages 1-29

  3. Binomial Random Variables

    • Yuan Shih Chow, Henry Teicher
    Pages 30-53

  4. Independence

    • Yuan Shih Chow, Henry Teicher
    Pages 54-83

  5. Integration in a Probability Space

    • Yuan Shih Chow, Henry Teicher
    Pages 84-112

  6. Sums of Independent Random Variables

    • Yuan Shih Chow, Henry Teicher
    Pages 113-158

  7. Measure Extensions, Lebesgue-Stieltjes Measure Kolmogorov Consistency Theorem

    • Yuan Shih Chow, Henry Teicher
    Pages 159-201

  8. Conditional Expectation, Conditional Independence, Introduction to Martingales

    • Yuan Shih Chow, Henry Teicher
    Pages 202-251

  9. Distribution Functions and Characteristic Functions

    • Yuan Shih Chow, Henry Teicher
    Pages 252-294

  10. Central Limit Theorems

    • Yuan Shih Chow, Henry Teicher
    Pages 295-335

  11. Limit Theorems for Independent Random Variables

    • Yuan Shih Chow, Henry Teicher
    Pages 336-385

  12. Martingales

    • Yuan Shih Chow, Henry Teicher
    Pages 386-423

  13. Infinitely Divisible Laws

    • Yuan Shih Chow, Henry Teicher
    Pages 424-457

  14. Back Matter

    Pages 458-467
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Keywords

About this book

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).

Authors and Affiliations

  • Department of Mathematical Statistics, Columbia University, New York, USA

    Yuan Shih Chow

  • Department of Statistics, Rutgers University, New Brunswick, USA

    Henry Teicher

Bibliographic Information

  • Book Title: Probability Theory

  • Book Subtitle: Independence, Interchangeability, Martingales

  • Authors: Yuan Shih Chow, Henry Teicher

  • Series Title: Springer Texts in Statistics

  • DOI: https://doi.org/10.1007/978-1-4684-0504-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1988

  • Softcover ISBN: 978-1-4684-0506-4Published: 02 February 2012

  • eBook ISBN: 978-1-4684-0504-0Published: 06 December 2012

  • Series ISSN: 1431-875X

  • Series E-ISSN: 2197-4136

  • Edition Number: 2

  • Number of Pages: XVIII, 467

  • Additional Information: Originally published as a monograph

  • Topics: Probability Theory and Stochastic Processes

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