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Probability Theory, Random Processes and Mathematical Statistics

  • Book
  • © 1995

Overview

Authors:
  1. Yu. A. Rozanov

    1. Steklov Mathematical Institute, Moscow, Russia

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Part of the book series: Mathematics and Its Applications (MAIA, volume 344)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introductory Probability Theory

    • Yu. A. Rozanov
    Pages 1-90

  3. Random Processes

    • Yu. A. Rozanov
    Pages 91-129

  4. An Introduction to Mathematical Statistics

    • Yu. A. Rozanov
    Pages 131-170

  5. Basic Elements of Probability Theory

    • Yu. A. Rozanov
    Pages 171-200

  6. Elements of Stochastic Analysis and Stochastic Differential Equations

    • Yu. A. Rozanov
    Pages 201-252

  7. Back Matter

    Pages 253-259
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Keywords

About this book

Probability Theory, Theory of Random Processes and Mathematical Statistics are important areas of modern mathematics and its applications. They develop rigorous models for a proper treatment for various 'random' phenomena which we encounter in the real world. They provide us with numerous tools for an analysis, prediction and, ultimately, control of random phenomena. Statistics itself helps with choice of a proper mathematical model (e.g., by estimation of unknown parameters) on the basis of statistical data collected by observations. This volume is intended to be a concise textbook for a graduate level course, with carefully selected topics representing the most important areas of modern Probability, Random Processes and Statistics. The first part (Ch. 1-3) can serve as a self-contained, elementary introduction to Probability, Random Processes and Statistics. It contains a number of relatively sim­ ple and typical examples of random phenomena which allow a natural introduction of general structures and methods. Only knowledge of elements of real/complex analysis, linear algebra and ordinary differential equations is required here. The second part (Ch. 4-6) provides a foundation of Stochastic Analysis, gives information on basic models of random processes and tools to study them. Here a familiarity with elements of functional analysis is necessary. Our intention to make this course fast-moving made it necessary to present important material in a form of examples.

Authors and Affiliations

  • Steklov Mathematical Institute, Moscow, Russia

    Yu. A. Rozanov

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