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Macmillan Higher Education Palgrave Higher Education

Probability Theory

ISBN 9781447152019
Publication Date June 2013
Formats Ebook Paperback 
Publisher Springer

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 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 make 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.

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.

Discrete Spaces of Elementary Events
An Arbitrary Space of Elementary Events
Random Variables and Distribution Functions
Numerical Characteristics of Random Variables
Sequences of Independent Trials with Two Outcomes
On Convergence of Random Variables and Distributions
Characteristic Functions
Sequences of Independent Random Variables. Limit Theorems
Large Deviation Probabilities for Sums of Independent Random Variables
Renewal Processes
Properties of the Trajectories of Random Walks. Zero-One Laws
Random Walks and Factorisation Identities
Sequences of Dependent Trials. Markov Chains
Information and Entropy
Martingales
Stationary Sequences
Stochastic Recursive Sequences
Continuous Time Random Processes
Processes with Independent Increments
Functional Limit Theorems
Markov Processes
Processes with Finite Second Moments. Gaussian Processes
Appendices.

Reviews

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 Högele, zbMATH, Vol. 1297, 2014)
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