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Probability Theory

Independence, Interchangeability, Martingales

  • Textbook
  • © 1997

Overview

Authors:
  1. Yuan Shih Chow

    1. Department of 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

  • A classic book, now in its third edition, is an essential reference to researchers and graduate students in probability theory
  • The new edition contains much new material, including U-statistic, additional theorems and examples, as well as simpler versions of some proofs

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

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xxii
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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 113-164

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

    • Yuan Shih Chow, Henry Teicher
    Pages 165-209

  8. Conditional Expectation, Conditional Independence, Introduction to Martingales

    • Yuan Shih Chow, Henry Teicher
    Pages 210-269

  9. Distribution Functions and Characteristic Functions

    • Yuan Shih Chow, Henry Teicher
    Pages 270-312

  10. Central Limit Theorems

    • Yuan Shih Chow, Henry Teicher
    Pages 313-353

  11. Limit Theorems for Independent Random Variables

    • Yuan Shih Chow, Henry Teicher
    Pages 354-403

  12. Martingales

    • Yuan Shih Chow, Henry Teicher
    Pages 404-443

  13. Infinitely Divisible Laws

    • Yuan Shih Chow, Henry Teicher
    Pages 444-477

  14. Back Matter

    Pages 479-489
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Keywords

About this book

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.

Authors and Affiliations

  • Department of 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/10.1007/978-1-4612-1950-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1997

  • Hardcover ISBN: 978-0-387-98228-1Published: 11 September 1997

  • Softcover ISBN: 978-0-387-40607-7Published: 17 October 2003

  • eBook ISBN: 978-1-4612-1950-7Published: 28 November 2012

  • Series ISSN: 1431-875X

  • Series E-ISSN: 2197-4136

  • Edition Number: 3

  • Number of Pages: XXII, 489

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Probability Theory and Stochastic Processes

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