Probability Theory: Independence, Interchangeability, Martingales

by Yuan S. Chow, Henry Teicher

Estimated delivery 3-12 business days

Format Paperback

Condition Brand New

Description This book is an introductory text on the beginning graduate level. Its subjects are the measure theoretical foundation of the theory and the main laws and theorems which emerge therefrom. The authors concentrate on certain important topics, primarily independence, interchangeability, and martingales. Particular emphasis is placed on stopping times, as tools in proving theorems as well as objects of interest in themselves. Among their applications is renewal theory; another useful application explained in this book is connected with the limiting behavior of random walks. A knowledge of measure theory is not assumed by the authors who intertwine measure and probability in their presentation as opposed to the customary sharp demarcation. The book can, however, be used as a text for students who have already been exposed to a course in measure theory. Many examples and exercises accompany the text.

Publisher Description

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).

Details

  • ISBN 1468405063
  • ISBN-13 9781468405064
  • Title Probability Theory: Independence, Interchangeability, Martingales
  • Author Yuan S. Chow, Henry Teicher
  • Format Paperback
  • Year 2012
  • Pages 467
  • Edition 2nd
  • Publisher Springer
  • Dimensions6.1 in. x 1 in. x 9.2 in.
GE_Item_ID:46825936;

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