Probability (Graduate Texts in Mathematics)
by A. N. Shiryayev
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Book Summary Information
Author: A. N. ShiryayevEdition: Hardcover
Audio: English (Unknown); English (Original Language); English (Published)
Published: 1984-02
ISBN: 0387908986
Number of pages: 577
Publisher: Springer-Verlag
Book Reviews of Probability (Graduate Texts in Mathematics)
Book Review: Wow!
Summary: 5 Stars
Almost everything has been said already by other reviewers, I am just going to confirm it really is that good. Starts from the very basics, builds theory up to startionary random processes, L2 theory, and some basic ergodic theorems, and gets you ready to learn the theory of random processes (which is not what this textbook is about). You'll have to find some other book as your "Part 2", I don't have any recommendations off-hand. However, for basic probability, in a rigorous setting, this is the book. He explains everything, and doesn't skip too many details, which is sweet. Proofs are easy to follow. However, I have found a few nasty typos which may have you bang your head against the wall. But you'll find them if you read carefully. Hopefully they will be corrected in subsequent printings. This shouldn't deter you. It really is an amazing book, in the russian tradition. See also Ya. Sinai's minibook on probability theory, many theorems are proved without the use of measure theory, so you can compare the proofs and get better insight into the machinery of those theorems.
Summary of Probability (Graduate Texts in Mathematics)
This book contains 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, ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy filter. Many examples are discussed in detail, and there are a large number of exercises. The book is accessible to advanced undergraduates and can be used as a text or for self-study.
The third edition contains new problems and exercises, new proofs, expanded material on financial mathematics, financial engineering, and mathematical statistics, and a final chapter on the history of probability theory.
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