 Along with Probability1, forms the third English edition of the author’s classic Probability
 Offers new problems, exercises, proofs, and applications in financial topics and mathematical statistics
 Features a Historical Review charting the development of the mathematical theory of probability
 Synthesizes classical ideas and results with many of the major achievements of modern probability theory
 Suitable for a course on random processes or for independent study
Buy this book
 About this Textbook

This textbook is the second volume of a pair that presents the latest English edition of the author’s classic, Probability. Building on the foundations established in the preceding Probability1, this volume guides the reader on to the theory of random processes. The new edition includes expanded material on financial mathematics and financial engineering; new problems, exercises, and proofs throughout; and a Historical Review charting the development of the mathematical theory of probability. Suitable for an advanced undergraduate or beginning graduate student with a course in probability theory, this volume forms the natural sequel to Probability1.
Probability2 opens with classical results related to sequences and sums of independent random variables, such as the zero–one laws, convergence of series, strong law of large numbers, and the law of the iterated logarithm. The subsequent chapters go on to develop the theory of random processes with discrete time: stationary processes, martingales, and Markov processes. The Historical Review illustrates the growth from intuitive notions of randomness in history through to modern day probability theory and theory of random processes.
Along with its companion volume, this textbook presents 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 throughout.
 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 recipient of the A.N. Kolmogorov Prize of the Russian Academy of Sciences in 1994 and the A.A. Markov Prize in 1974. His numerous other titles include Problems in Probability, translated by A. Lyasoff, which offers more than 1500 exercises and problems as a supplement to Probability.
Translator 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 and is the translator of over 6 volumes from Russian to English.  Video

 Table of contents (5 chapters)


Sequences and Sums of Independent Random Variables
Pages 132

Stationary (Strict Sense) Random Sequences and Ergodic Theory
Pages 3346

Stationary (Wide Sense) Random Sequences: L 2Theory
Pages 47106

Martingales
Pages 107235

Markov Chains
Pages 237312

Table of contents (5 chapters)
Buy this book
Services for this Book
Recommended for you
Bibliographic Information
 Bibliographic Information

 Book Title
 Probability2
 Authors

 Albert N. Shiryaev
 Translated by
 Chibisov, D.M.
 Series Title
 Graduate Texts in Mathematics
 Series Volume
 95
 Copyright
 2019
 Publisher
 SpringerVerlag New York
 Copyright Holder
 Springer Science+Business Media, LLC, part of Springer Nature
 Distribution Rights
 Distribution rights for India: Researchco Book Centre, New Delhi, India
 eBook ISBN
 9780387722085
 DOI
 10.1007/9780387722085
 Hardcover ISBN
 9780387722078
 Series ISSN
 00725285
 Edition Number
 3
 Number of Pages
 X, 348
 Number of Illustrations
 16 b/w illustrations
 Additional Information
 Originally published in one volume; English translation of the 4th original Russian edition published by © Shiryaev A. N., 2007 and © MCCME, 2007
 Topics