 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
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 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 measuretheoretic 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 inclusionexclusion principle, theorems on monotonic classes (relying on a detailed treatment of “πλ” 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 EditorinChief of the journal Mathematical Methods of Statistics.  Reviews

“This book is axiomatic and abstract, and presents a comprehensive but puremath 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)
“This book provides a general introduction to probability theory, and covers several advanced topics. … Numerous examples and problems help the reader to understand the topics. The book is recommended to master and PhD students in mathematics.” (László Viharos, Acta Scientiarum Mathematicarum, Vol. 83 (12), 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 wellmotivated, 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
Pages 1158

Mathematical Foundations of Probability Theory
Pages 159371

Convergence of Probability Measures. Central Limit Theorem
Pages 373460

Table of contents (3 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Probability1
 Authors

 Albert N. Shiryaev
 Translated by
 Chibisov, D.M.
 Series Title
 Graduate Texts in Mathematics
 Series Volume
 95
 Copyright
 2016
 Publisher
 SpringerVerlag New York
 Copyright Holder
 Springer Science+Business Media New York
 eBook ISBN
 9780387722061
 DOI
 10.1007/9780387722061
 Hardcover ISBN
 9780387722054
 Softcover ISBN
 9781493979059
 Series ISSN
 00725285
 Edition Number
 3
 Number of Pages
 XVII, 486
 Number of Illustrations
 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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