Overview
- Along with Probability-1, 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
Part of the book series: Graduate Texts in Mathematics (GTM, volume 95)
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Table of contents (5 chapters)
Keywords
- probability theory
- random processes
- discrete time processes
- random sequences
- probability textbook
- random processes textbook
- sums of independent random variables
- stationary random sequences
- random sequences
- martingales
- Markov chains
- zero-one laws
- convergence of series
- strong law of large numbers
- law of the iterated logarithm
- financial mathematics
- financial engineering
About this book
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 Probability-1, 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 Probability-1.
Probability-2 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 measure-theoretic 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.
Reviews
Authors and Affiliations
About the author
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 Editor-in-Chief of the journal Mathematical Methods of Statistics and is the translator of over 6 volumes from Russian to English.
Bibliographic Information
Book Title: Probability-2
Authors: Albert N. Shiryaev
Translated by: Dmitry M. Chibisov
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-0-387-72208-5
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2019
Hardcover ISBN: 978-0-387-72207-8Published: 25 March 2019
Softcover ISBN: 978-1-0716-1829-5Published: 21 July 2021
eBook ISBN: 978-0-387-72208-5Published: 23 March 2019
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
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