Probability Theory is a classic topic in any course of exact sciences, that evolved from the amalgamation of different areas of mathematics, including set and measure theory. An axiomatic treatment of probability is presented in the book. Probability Theory is fundamental to several areas of knowledge, including engineering, computer science, mathematics, physics, sciences, economics, biology, medicine, social sciences and social communication. The book targets graduate students who may not have taken basic courses in these specific topics, and can provide a quick and concise way to obtain the knowledge they need to succeed in advanced courses.

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.