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Probability Theory (Universitext), by Alexander A. Borovkov
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Probability theory is an actively developing branch of mathematics. It has applications in many areas of science and technology and forms the basis of mathematical statistics. This self-contained, comprehensive book tackles the principal problems and advanced questions of probability theory and random processes in 22 chapters, presented in a logical order but also suitable for dipping into. They include both classical and more recent results, such as large deviations theory, factorization identities, information theory, stochastic recursive sequences. The book is further distinguished by the inclusion of clear and illustrative proofs of the fundamental results that comprise many methodological improvements aimed at simplifying the arguments and making them more transparent.
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The importance of the Russian school in the development of probability theory has long been recognized. This book is the translation of the fifth edition of the highly successful and esteemed Russian textbook. This edition includes a number of new sections, such as a new chapter on large deviation theory for random walks, which are of both theoretical and applied interest. The frequent references to Russian literature throughout this work lend a fresh dimension and makes it an invaluable source of reference for Western researchers and advanced students in probability related subjects.
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Probability Theory will be of interest to both advanced undergraduate and graduate students studying probability theory and its applications. It can serve as a basis for several one-semester courses on probability theory and random processes as well as self-study.
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About the Author
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Professor Alexandr Borovkov lives and works in the Novosibirsk Academy Town in Russia and is affiliated with both the Sobolev Institute of Mathematics of the Russian Academy of Sciences and the Novosibirsk State University. He is one of the most prominent Russian specialists in probability theory and mathematical statistics. Alexandr Borovkov authored and co-authored more than 200 research papers and ten research monographs and advanced level university textbooks. His contributions to mathematics and its applications are widely recognized, which included election to the Russian Academy of Sciences and several prestigious awards for his research and textbooks.
- Sales Rank: #2467584 in Books
- Published on: 2013-06-21
- Released on: 2013-06-21
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 1.73" w x 6.13" l, 2.32 pounds
- Binding: Paperback
- 733 pages
Review
From the book reviews:
“The current version of the book contains twenty-two chapters and seven appendices. … the book may well serve as the basis of up to four consecutive, mainly undergraduate probability courses. Although in the last years many new topics in probability theory have gained a lot of attention, the present author’s account is a precious self-contained standard reference, which preserves and prolongs the excellence of the Soviet probability education to our days.” (Michael H�gele, zbMATH, Vol. 1297, 2014)
From the Back Cover
Probability theory is an actively developing branch of mathematics. It has applications in many areas of science and technology and forms the basis of mathematical statistics. This self-contained, comprehensive book tackles the principal problems and advanced questions of probability theory and random processes in 22 chapters, presented in a logical order but also suitable for dipping into. They include both classical and more recent results, such as large deviations theory, factorization identities, information theory, stochastic recursive sequences. The book is further distinguished by the inclusion of clear and illustrative proofs of the fundamental results that comprise many methodological improvements aimed at simplifying the arguments and making them more transparent.
�
The importance of the Russian school in the development of probability theory has long been recognized. This book is the translation of the fifth edition of the highly successful and esteemed Russian textbook. This edition includes a number of new sections, such as a new chapter on large deviation theory for random walks, which are of both theoretical and applied interest. The frequent references to Russian literature throughout this work lend a fresh dimension and makes it an invaluable source of reference for Western researchers and advanced students in probability related subjects.
�
Probability Theory will be of interest to both advanced undergraduate and graduate students studying probability theory and its applications. It can serve as a basis for several one-semester courses on probability theory and random processes as well as self-study.
�
About the Author
�
Professor Alexandr Borovkov lives and works in the Novosibirsk Academy Town in Russia and is affiliated with both the Sobolev Institute of Mathematics of the Russian Academy of Sciences and the Novosibirsk State University. He is one of the most prominent Russian specialists in probability theory and mathematical statistics. Alexandr Borovkov authored and co-authored more than 200 research papers and ten research monographs and advanced level university textbooks. His contributions to mathematics and its applications are widely recognized, which included election to the Russian Academy of Sciences and several prestigious awards for his research and textbooks.
Most helpful customer reviews
39 of 39 people found the following review helpful.
An excellent graduate course in probability
By Stanislav Kolenikov
(This review is based on the second Russian edition printed in 1986. The contents of English edition seems to be a bit extended version of the Russian one.)
This is a very good exposition to probability theory at the professional level. I like it much more than I do Billingsley's "Probability and Measure" (which is a collection of essays on probability theory, sometimes only vaguely related a few chapters apart from each other, while Borovkov is a very consistent course which has the same level of rigor as Billingsley does, and which also proves some subtle but appreciable things not mentioned in Billingsley). It has a bit different flavor of tending to prove things via characteristic functions rather than directly with the cesnored random variables as in Billinsley's book. It does not cover as much measure theory as Billingsley does, and I suspect that the book implicitly assumes the student to be familiar with a standard Russian reference on functional analysis by Kolmogorov and Fomin that has an extensive treatment of Lebesgue integration. It is also nice that it has a lot of examples discussed in the text (rather than given as exercises) that help to cement the concepts. They make the text quite lively, too. Sometimes I had to spend a minute or two thinking why they believe a statement in a proof is self-evident, though.
The book starts with with the introduction of probability spaces, goes on to random variables, then to the laws of large numbers, convergence notions, and the CLTs. It also discusses renewal theory, factorization identities, Markov chains, information and entropy, martingales, continuous time stocastic processes, functional limit theorems, and Markov processes, with some measure theory stuff and a couple of more difficult theorems (extension of a measure, Kolmogorov theorem on consistent distributions, theorems of Helly and Arcela--Ascoli) given in appendices. Thus it covers more than a semester of probability theory, giving some initial reading for some four or so advanced courses. The author suggests to use the bulk of the material in the first ten or twelve chapters for a required semester course, with the rest of the book viewed as the material for shorter elective courses. The book helped me greatly in my probability theory comprehensive exam, as well as in my stochastic calculus and stochastic processes courses.
It is a pity that the book is rather expensive -- I am happy to have it in the original language on which this review is actually based.
Of historical interest it is that A.Borovkov is Kolmogorov's student.
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