Springer Texts in Statistics

Probability Theory

Independence, Interchangeability, Martingales

Authors: Chow, Yuan Shih, Teicher, Henry

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eBook $59.99
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  • ISBN 978-1-4612-1950-7
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Hardcover $99.00
price for USA
  • ISBN 978-0-387-98228-1
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Softcover $79.99
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  • ISBN 978-0-387-40607-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

Table of contents (12 chapters)

  • Classes of Sets, Measures, and Probability Spaces

    Chow, Yuan Shih (et al.)

    Pages 1-29

  • Binomial Random Variables

    Chow, Yuan Shih (et al.)

    Pages 30-53

  • Independence

    Chow, Yuan Shih (et al.)

    Pages 54-83

  • Integration in a Probability Space

    Chow, Yuan Shih (et al.)

    Pages 84-112

  • Sums of Independent Random Variables

    Chow, Yuan Shih (et al.)

    Pages 113-164

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4612-1950-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-0-387-98228-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA
  • ISBN 978-0-387-40607-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Probability Theory
Book Subtitle
Independence, Interchangeability, Martingales
Authors
Series Title
Springer Texts in Statistics
Copyright
1997
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1950-7
DOI
10.1007/978-1-4612-1950-7
Hardcover ISBN
978-0-387-98228-1
Softcover ISBN
978-0-387-40607-7
Series ISSN
1431-875X
Edition Number
3
Number of Pages
XXII, 489
Number of Illustrations and Tables
1 b/w illustrations
Topics