Probability-2

• Albert N. Shiryaev Part of the Graduate Texts in Mathematics book series (GTM, volume 95)

1. Front Matter
Pages i-x
2. Albert N. Shiryaev
Pages 1-32
3. Albert N. Shiryaev
Pages 33-46
4. Albert N. Shiryaev
Pages 47-106
5. Albert N. Shiryaev
Pages 107-235
6. Albert N. Shiryaev
Pages 237-312
7. Back Matter
Pages 313-348

Introduction

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.

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

Authors and affiliations

• Albert N. Shiryaev
• 1
1. 1.Department of Probability Theory and Mathematical StatisticsSteklov Mathematical Institute and Lomonosov Moscow State UniversityMoscowRussia

Bibliographic information

• DOI https://doi.org/10.1007/978-0-387-72208-5
• Copyright Information Springer Science+Business Media, LLC, part of Springer Nature 2019
• Publisher Name Springer, New York, NY
• eBook Packages Mathematics and Statistics
• Print ISBN 978-0-387-72207-8
• Online ISBN 978-0-387-72208-5
• Series Print ISSN 0072-5285
• Series Online ISSN 2197-5612
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