Graduate Texts in Mathematics

Probability-1

Authors: Shiryaev, Albert N.

  • Successfully synthesizes the most important classical ideas and results with many of the major achievements of modern probability theory
  • Author provides clear and comprehensive introduction to probability theory
  • Third edition now has a chapter on the history of probability theory
  • Covers in detail topics including ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy filter
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eBook $59.99
price for USA (gross)
  • ISBN 978-0-387-72206-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-0-387-72205-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, the measure-theoretic foundations of probability theory, weak convergence of probability measures, and the central limit theorem. Many examples are discussed in detail, and there are a large number of exercises. The book is accessible to advanced undergraduates and can be used as a text for independent study.

To accommodate the greatly expanded material in the third edition of Probability, the book is now divided into two volumes. This first volume contains updated references and substantial revisions of the first three chapters of the second edition. In particular, new material has been added on generating functions, the inclusion-exclusion principle, theorems on monotonic classes (relying on a detailed treatment of “π-λ” systems), and the fundamental theorems of mathematical statistics.

About the authors

Albert N. Shiryaev is Chief Scientific Researcher and Professor of Probability Theory and Mathematical Statistics at the Steklov Mathematical Institute of the Russian Academy of Sciences and Head of the Department of Probability Theory in the Mechanics and Mathematics Faculty at Lomonosov Moscow State University. He is the author of several books, including Problems in Probability [translated by Andrew Lyasov], Optimal Stopping Rules [translated by A.B. Aries], and Statistics of Random Processes [with Robert S. Liptser]. He was the recipient of the A.N. Kolmogorov Prize of the Russian Academy of Sciences in 1994 and the A.A. Markov Prize in 1974.

Dmitry M. Chibisov is Leading Scientific Researcher and Professor of Probability Theory and Mathematical Statistics at the Steklov Mathematical Institute of the Russian Academy of Sciences. He is the Editor-in-Chief of the journal Mathematical Methods of Statistics.

Reviews

“This book is axiomatic and abstract, and presents a comprehensive but pure-math approach to probability theory. … There are good exercises throughout the book … . I think this is a good book if you like this kind of very abstract approach.” (Allen Stenger, MAA Reviews, August, 2017)

It is clear that this book contains important and interesting results obtained through a long time period, beginning with the classical Bernoulli's law of large numbers, and ending with very recent results concerning convergence of martingales and absolute continuity of probability measures. Let us note especially that the great number of ideas, notions and statements in the book are well-motivated, explained in detail and illustrated by suitably chosen examples and a large number of exercises. Thus, the present book is a synthesis of all significant classical ideas and results, and many of the major achievements of modern probability theory. In the whole it is a welcome addition to mathematical literature and can become an indispensable textbook for courses in stochastics.

- J. Stoyanov, Zentralblatt

 


Table of contents (3 chapters)

  • Elementary Probability Theory

    Shiryaev, Albert N.

    Pages 1-158

  • Mathematical Foundations of Probability Theory

    Shiryaev, Albert N.

    Pages 159-371

  • Convergence of Probability Measures. Central Limit Theorem

    Shiryaev, Albert N.

    Pages 373-460

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-0-387-72206-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-0-387-72205-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Probability-1
Authors
Translated by
Chibisov, D.M.
Series Title
Graduate Texts in Mathematics
Series Volume
95
Copyright
2016
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-387-72206-1
DOI
10.1007/978-0-387-72206-1
Hardcover ISBN
978-0-387-72205-4
Series ISSN
0072-5285
Edition Number
3
Number of Pages
XVII, 486
Number of Illustrations and Tables
39 b/w illustrations
Additional Information
Originally published in one volume. Translated from the 4th Russian edition (2007); 3rd Russian Edition 2004, 2nd Russian Edition 1989, 1st Russian Edition 1980. Previous English translations: 2nd Edition 1996, 1st Edition 1984.
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