Probability

1. Front Matter

   Pages i-xvi

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2. Introduction

   • A. N. Shiryaev

   Pages 1-4

3. Elementary Probability Theory

   • A. N. Shiryaev

   Pages 5-130

4. Mathematical Foundations of Probability Theory

   • A. N. Shiryaev

   Pages 131-307

5. Convergence of Probability Measures. Central Limit Theorem

   • A. N. Shiryaev

   Pages 308-378

6. Sequences and Sums of Independent Random Variables

   • A. N. Shiryaev

   Pages 379-403

7. Stationary (Strict Sense) Random Sequences and Ergodic Theory

   • A. N. Shiryaev

   Pages 404-414

8. Stationary (Wide Sense) Random Sequences. L ²-Theory

   • A. N. Shiryaev

   Pages 415-473

9. Sequences of Random Variables That Form Martingales

   • A. N. Shiryaev

   Pages 474-563

10. Sequences of Random Variables That Form Markov Chains

    • A. N. Shiryaev

    Pages 564-595

11. Back Matter

    Pages 597-624

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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.

• Ergodic theory
• Markov chain
• Martingale
• Probability theory
• Random variable
• Stochastic processes
• random walk
• stochastic process

• Steklov Mathematical Institute, Moscow, Russia

  A. N. Shiryaev

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