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Probability

  • Textbook
  • © 1984

Overview

Authors:
  1. A. N. Shiryayev

    1. Steklov Mathematical Institute, Moscow, USSR

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 95)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    • A. N. Shiryayev
    Pages 1-4

  3. Elementary Probability Theory

    • A. N. Shiryayev
    Pages 5-128

  4. Mathematical Foundations of Probability Theory

    • A. N. Shiryayev
    Pages 129-305

  5. Convergence of Probability Measures. Central Limit Theorem

    • A. N. Shiryayev
    Pages 306-353

  6. Sequences and Sums of Independent Random Variables

    • A. N. Shiryayev
    Pages 354-375

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

    • A. N. Shiryayev
    Pages 376-386

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

    • A. N. Shiryayev
    Pages 387-445

  9. Sequences of Random Variables That Form Martingales

    • A. N. Shiryayev
    Pages 446-522

  10. Sequences of Random Variables That Form Markov Chains

    • A. N. Shiryayev
    Pages 523-554

  11. Back Matter

    Pages 555-580
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Keywords

About this book

This textbook is based on a three-semester course of lectures given by the author in recent years in the Mechanics-Mathematics Faculty of Moscow State University and issued, in part, in mimeographed form under the title Probability, Statistics, Stochastic Processes, I, II by the Moscow State University Press. We follow tradition by devoting the first part of the course (roughly one semester) to the elementary theory of probability (Chapter I). This begins with the construction of probabilistic models with finitely many outcomes and introduces such fundamental probabilistic concepts as sample spaces, events, probability, independence, random variables, expectation, corre­ lation, conditional probabilities, and so on. Many probabilistic and statistical regularities are effectively illustrated even by the simplest random walk generated by Bernoulli trials. In this connection we study both classical results (law of large numbers, local and integral De Moivre and Laplace theorems) and more modern results (for example, the arc sine law). The first chapter concludes with a discussion of dependent random vari­ ables generated by martingales and by Markov chains.

Authors and Affiliations

  • Steklov Mathematical Institute, Moscow, USSR

    A. N. Shiryayev

Bibliographic Information

  • Book Title: Probability

  • Authors: A. N. Shiryayev

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4899-0018-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1984

  • eBook ISBN: 978-1-4899-0018-0Published: 29 June 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XI, 580

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Probability Theory and Stochastic Processes

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