Probability (Graduate Texts in Mathematics) (v. 95) [Hardcover]

Albert N. Shiryaev (Author), R. P. Boas (Translator)

Book Description

ISBN-10: 0387945490 | ISBN-13: 978-0387945491 | Publication Date: December 8, 1995 | Edition: 2nd

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 for self-study. This new edition contains substantial revisions and updated references. The reader will find a deeper study of topics such as the distance between probability measures, metrization of weak convergence, and contiguity of probability measures. Proofs for a number of some important results which were merely stated in the first edition have been added. The author included new material on the probability of large deviations, and on the central limit theorem for sums of dependent random variables.

Editorial Reviews

Review

About the First English Edition:

It is clear that this book contains important and interesting results obtained through a long time period, beginning with the classical Bernoulli's law of large numbers, and ending with very recent results concerning convergence of martingales and absolute continuity of probability measures. Let us note especially that the great number of ideas, notions and statements in the book are well-motivated, explained in detail and illustrated by suitably chosen examples and a large number of exercises. Thus, the present book is a synthesis of all significant classical ideas and results, and many of the major achievements of modern probability theory. In the whole it is a welcome addition to mathematical literature and can become an indispensable textbook for courses in stochastics.

- J. Stoyanov, Zentralblatt

--This text refers to an alternate Hardcover edition.

Language Notes

Text: English (translation)
Original Language: Russian

Product Details

• Hardcover: 637 pages
• Publisher: Springer; 2nd edition (December 8, 1995)
• Language: English
• ISBN-10: 0387945490
• ISBN-13: 978-0387945491
• Product Dimensions: 9.3 x 6.2 x 1.3 inches
• Shipping Weight: 2.2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (12 customer reviews)
• Amazon Best Sellers Rank: #436,965 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

43 of 46 people found the following review helpful:

5.0 out of 5 stars Recommended for researchers in probability and statistics, March 11, 2002

By 

Todd Ebert (Long Beach California) - See all my reviews

This review is from: Probability (Graduate Texts in Mathematics) (v. 95) (Hardcover)

The most important quality to note about this book is that it is *indeed* a graduate textbook. Thus, anyone who is considering reading this book and who has not yet studied ideas such as random processes (including Markov chains and martingales), the Central Limit Theorem, etc.. should pass on this book and look into one or more undergraduate texts (Ross's "Probability Models" would make a good start). Another question the potential buyer should ask is, "Do I want to apply probability, or do I want to study probability for the sake of probability?". If it is the former, then there are many more suitable books whose union covers all the topics in this book, and does so in a much more clear and inuitive manner (For example, "Ergodic Theory" by Halmos, "Probability Models" and "Random Processes" by Ross, and "Mathematical Statistics Chapters 1-8" by Roussas is one example of such a covering). On the other hand, if the answer is the latter, then stop here and begin reading! In other words, the 5 stars for this review is relative to anticipating that the reader is a grad. student who wants to do research in probability and/or statistics. Conditioning on these assumptions, the clarity and coverage found in this text cannot be matched. The measure-theoretic approach may take some time to get used to, but in the end the reader will be thankful for this, as many of the proofs fall out quite easily.

15 of 15 people found the following review helpful:

5.0 out of 5 stars A complete course in probability, March 10, 2002

By 

Juan Pablo Pardo G (Mexico City (Physics Undergrad)) - See all my reviews

This review is from: Probability (Graduate Texts in Mathematics) (v. 95) (Hardcover)

When I started to develop an interest in statistics and probability I took the challenge of finding a concise probability book that balanced both the formal aspects of the theory as the practical approach. After many books, I decided to take a look a springer-verlag's related texts. I was surprised when I found this book since, even though its name (Graduate Texts in Mathematics, me being an undergrad), it is a down-to-earth book that takes by the hand through probability theory. Among the many books I read, (in some cases just tried to read), Shiryaev's book was the most organized and efficient one: it didn't lose valuable time explaining obvious concepts nor did it overshadow the underlying ideas with complex mathematical formalisms: it was simple and comprehensive. I think this book is highly recommendable to any science student familiarized with the most essential mathematical concepts, who wishes to have in the bookshelf and near of hand a complete probability course (in reality, the only knowledge needed is elementary calculus, series, and a set theory and a very basic notion of probability doesn't hurt). This book, in combination with an applied probability book, is more than enough to understand this fascinating and necessary subjet (I also recommend in adition to this text, "Mathematical Statistics" by Terrell, also a Springer-Verlag)

11 of 11 people found the following review helpful:

5.0 out of 5 stars A great probability book for both undergraduate and graduate learners, March 13, 2006

By 

Vuong Quan Hoang (Hanoi, Viet Nam) - See all my reviews
(REAL NAME)   

This review is from: Probability (Graduate Texts in Mathematics) (v. 95) (Hardcover)

I write this to pay my highest respects for this guru mathematician's work. This is truly a great book, not only for graduate students but also undergraduate and researchers. The book covers 8 chapters, starting with classic approach, so that one can see the evolution of the theory of probability, and one could avoid the risk of being lost in this forest.

It has a particularly useful Chapter 2, which provides the readers with necessary mathematical foundation for them to go on. Of course, the theory itself is challenging and we will/should never expect an easy-to-read mathematics book. The transformation from classical approach to the modern one is exhibited clearly by this great Russian mathematician. You will find almost everything in here, even some critical part that touches on stochastic differential equations, that are very useful for applied fields of sciences such as mathematical finance.

Index of keywords is also very useful and in details. We should also notice that the book is not too thick compared to other multi-volume textbooks. This is a real advantage if you have to carry it along while working or when reading for leisure.

However, be careful with some examples and solutions. I found at least one problem in which Prof. Shiryaev provided wrong solution, e.g. problem on girl vs boy child on page 25 of 2nd Edition. The final result is correct, but the evolution shows a wrong method.

Despite this minor thing, a matter of Buyer Beware, I find it a really great book that has accompanied me for over 7 years now. It is worth every penny. Thus do not waste your money on others before trying this. You will agree with me at the end. The book is a piece of art!