Probability: v. 95 (Graduate Texts in Mathematics) - Hardcover

Shiryaev, Albert N.

Hardcover

ISBN 10: 0387945490 ISBN 13: 9780387945491

Publisher: Springer-Verlag New York Inc., 1995

Synopsis

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.

About this title

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

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.

Edition details

• Publisher: Springer-Verlag New York Inc.
• Publication date: 1995
• Language: English
• ISBN 10: 0387945490
• ISBN 13: 9780387945491
• Binding: Hardcover
• Edition number: 2
• Number of pages: 640