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Probability (Graduate Texts in Mathematics) (v. 95), by Albert N. Shiryaev
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In the Preface to the first edition, originally published in 1980, we mentioned that this book was based on the author's lectures in the Department of Mechanics and Mathematics of the Lomonosov University in Moscow, which were issued, in part, in mimeographed form under the title "Probabil ity, Statistics, and Stochastic Processors, I, II" and published by that Univer sity. Our original intention in writing the first edition of this book was to divide the contents into three parts: probability, mathematical statistics, and theory of stochastic processes, which corresponds to an outline of a three semester course of lectures for university students of mathematics. However, in the course of preparing the book, it turned out to be impossible to realize this intention completely, since a full exposition would have required too much space. In this connection, we stated in the Preface to the first edition that only probability theory and the theory of random processes with discrete time were really adequately presented. Essentially all of the first edition is reproduced in this second edition. Changes and corrections are, as a rule, editorial, taking into account com ments made by both Russian and foreign readers of the Russian original and ofthe English and Germantranslations [Sll]. The author is grateful to all of these readers for their attention, advice, and helpful criticisms. In this second English edition, new material also has been added, as follows: in Chapter 111, §5, §§7-12; in Chapter IV, §5; in Chapter VII, §§8-10.
- Sales Rank: #951938 in Books
- Published on: 1995-12-08
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.38" w x 6.14" l, 2.25 pounds
- Binding: Hardcover
- 624 pages
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
Language Notes
Text: English (translation)
Original Language: Russian
From the Back Cover
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 has included new material on the probability of large deviations, on the central limit theorem for sums of dependent random variables, and on a discrete version of Ito's formula.
Most helpful customer reviews
0 of 0 people found the following review helpful.
come to this book and you will taste the real fun.
By José VinÃcius de Miranda Cardoso
After you get the basics of intuitive probability, come to this book and you will taste the real fun.
15 of 16 people found the following review helpful.
The name should be "Basics of the probability"
By S.O.O.
It covers almost all of the "basic" ideas in probability.
This book is one of the most helpful book for me. You will "learn" what is going on in the field of probability theory. The book is especially suitable for self studying. If you want to learn probability theory, buy this book, dig into it, study again and again if you don't understand a particular part. But the book does its best in terms of clarity of exposition, so you can understand with a careful reading.
It will provide a strong tool and you can use this tool efficiently in your professional career. But there is a caveat. You might end up with a tool that you will never use again. The book is suitable for professionals and deep minds.
18 of 19 people found the following review helpful.
A great probability book for both undergraduate and graduate learners
By Amazon Customer
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!
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