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
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This book gives an introduction to probability and its many practical application by providing a thorough, entertaining account of basic probability and important random processes, covering a range of important topics. Emphasis is on modelling rather than abstraction and there are new sections on sampling and Markov chain Monte Carlo, renewal-reward, queueing networks, stochastic calculus, and option pricing in the Black-Scholes model for financial markets. In addition, there are almost 400 exercises and problems relevant to the material. Solutions can be found in One Thousand Exercises in Probability.
