Ebook: Probability Theory

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.

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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.

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.

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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.

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.

Content:
Front Matter....Pages I-XXVIII
Discrete Spaces of Elementary Events....Pages 1-11
An Arbitrary Space of Elementary Events....Pages 13-29
Random Variables and Distribution Functions....Pages 31-63
Numerical Characteristics of Random Variables....Pages 65-105
Sequences of Independent Trials with Two Outcomes....Pages 107-127
On Convergence of Random Variables and Distributions....Pages 129-151
Characteristic Functions....Pages 153-184
Sequences of Independent Random Variables. Limit Theorems....Pages 185-238
Large Deviation Probabilities for Sums of Independent Random Variables....Pages 239-276
Renewal Processes....Pages 277-313
Properties of the Trajectories of Random Walks. Zero-One Laws....Pages 315-332
Random Walks and Factorisation Identities....Pages 333-387
Sequences of Dependent Trials. Markov Chains....Pages 389-446
Information and Entropy....Pages 447-456
Martingales....Pages 457-492
Stationary Sequences....Pages 493-506
Stochastic Recursive Sequences....Pages 507-526
Continuous Time Random Processes....Pages 527-537
Processes with Independent Increments....Pages 539-557
Functional Limit Theorems....Pages 559-577
Markov Processes....Pages 579-609
Processes with Finite Second Moments. Gaussian Processes....Pages 611-618
Back Matter....Pages 619-733

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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.

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.

Content:
Front Matter....Pages I-XXVIII
Discrete Spaces of Elementary Events....Pages 1-11
An Arbitrary Space of Elementary Events....Pages 13-29
Random Variables and Distribution Functions....Pages 31-63
Numerical Characteristics of Random Variables....Pages 65-105
Sequences of Independent Trials with Two Outcomes....Pages 107-127
On Convergence of Random Variables and Distributions....Pages 129-151
Characteristic Functions....Pages 153-184
Sequences of Independent Random Variables. Limit Theorems....Pages 185-238
Large Deviation Probabilities for Sums of Independent Random Variables....Pages 239-276
Renewal Processes....Pages 277-313
Properties of the Trajectories of Random Walks. Zero-One Laws....Pages 315-332
Random Walks and Factorisation Identities....Pages 333-387
Sequences of Dependent Trials. Markov Chains....Pages 389-446
Information and Entropy....Pages 447-456
Martingales....Pages 457-492
Stationary Sequences....Pages 493-506
Stochastic Recursive Sequences....Pages 507-526
Continuous Time Random Processes....Pages 527-537
Processes with Independent Increments....Pages 539-557
Functional Limit Theorems....Pages 559-577
Markov Processes....Pages 579-609
Processes with Finite Second Moments. Gaussian Processes....Pages 611-618
Back Matter....Pages 619-733
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