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Introduction to Random Processes

  • Book
  • © 1987

Overview

Authors:
  1. Yuriĭ A. Rozanov

    1. Steklov Mathematical Institute, Moscow, USSR

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Part of the book series: Springer Series in Soviet Mathematics (SSSOV)

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-VIII
    Download chapter PDF

  2. Random Processes with Discrete State Space

    • Yuriĭ A. Rozanov
    Pages 1-9

  3. Homogeneous Markov Processes with a Countable Number of States

    • Yuriĭ A. Rozanov
    Pages 10-17

  4. Homogeneous Markov Processes with a Countable Number of States

    • Yuriĭ A. Rozanov
    Pages 18-24

  5. Branching Processes

    • Yuriĭ A. Rozanov
    Pages 25-32

  6. Brownian Motion

    • Yuriĭ A. Rozanov
    Pages 33-43

  7. Random Processes in Multi-Server Systems

    • Yuriĭ A. Rozanov
    Pages 44-51

  8. Random Processes as Functions in Hilbert Space

    • Yuriĭ A. Rozanov
    Pages 52-56

  9. Stochastic Measures and Integrals

    • Yuriĭ A. Rozanov
    Pages 57-60

  10. The Stochastic Ito Integral and Stochastic Differentials

    • Yuriĭ A. Rozanov
    Pages 61-67

  11. Stochastic Differential Equations

    • Yuriĭ A. Rozanov
    Pages 68-72

  12. Diffusion Processes

    • Yuriĭ A. Rozanov
    Pages 73-76

  13. Linear Stochastic Differential Equations and Linear Random Processes

    • Yuriĭ A. Rozanov
    Pages 77-83

  14. Stationary Processes

    • Yuriĭ A. Rozanov
    Pages 84-91

  15. Some Problems of Optimal Estimation

    • Yuriĭ A. Rozanov
    Pages 92-99

  16. A Filtration Problem

    • Yuriĭ A. Rozanov
    Pages 100-117

  17. Back Matter

    Pages 108-120
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Keywords

About this book

Today, the theory of random processes represents a large field of mathematics with many different branches, and the task of choosing topics for a brief introduction to this theory is far from being simple. This introduction to the theory of random processes uses mathematical models that are simple, but have some importance for applications. We consider different processes, whose development in time depends on some random factors. The fundamental problem can be briefly circumscribed in the following way: given some relatively simple characteristics of a process, compute the probability of another event which may be very complicated; or estimate a random variable which is related to the behaviour of the process. The models that we consider are chosen in such a way that it is possible to discuss the different methods of the theory of random processes by referring to these models. The book starts with a treatment of homogeneous Markov processes with a countable number of states. The main topic is the ergodic theorem, the method of Kolmogorov's differential equations (Secs. 1-4) and the Brownian motion process, the connecting link being the transition from Kolmogorov's differential-difference equations for random walk to a limit diffusion equation (Sec. 5).

Authors and Affiliations

  • Steklov Mathematical Institute, Moscow, USSR

    Yuriĭ A. Rozanov

Bibliographic Information

  • Book Title: Introduction to Random Processes

  • Authors: Yuriĭ A. Rozanov

  • Series Title: Springer Series in Soviet Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-72717-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • Softcover ISBN: 978-3-642-72719-1Published: 06 December 2011

  • eBook ISBN: 978-3-642-72717-7Published: 06 December 2012

  • Series ISSN: 0939-1169

  • Edition Number: 1

  • Number of Pages: VIII, 117

  • Additional Information: Original Russian edition published by Nauka, Moscow 1982

  • Topics: Probability Theory and Stochastic Processes

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