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Random Perturbations of Dynamical Systems

  • Book
  • © 1984

Overview

Authors:
  1. M. I. Freidlin

    1. VAAP Copyright Agency of the U.S.S.R., Moscow, USSR

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    You can also search for this author in PubMed   Google Scholar

  2. A. D. Wentzell

    1. VAAP Copyright Agency of the U.S.S.R., Moscow, USSR

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 260)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Introduction

    • M. I. Freidlin, A. D. Wentzell
    Pages 1-14

  3. Random Perturbations

    • M. I. Freidlin, A. D. Wentzell
    Pages 15-43

  4. Small Random Perturbations on a Finite Time Interval

    • M. I. Freidlin, A. D. Wentzell
    Pages 44-69

  5. Action Functional

    • M. I. Freidlin, A. D. Wentzell
    Pages 70-102

  6. Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point

    • M. I. Freidlin, A. D. Wentzell
    Pages 103-135

  7. Perturbations Leading to Markov Processes

    • M. I. Freidlin, A. D. Wentzell
    Pages 136-160

  8. Markov Perturbations on Large Time Intervals

    • M. I. Freidlin, A. D. Wentzell
    Pages 161-211

  9. The Averaging Principle. Fluctuations in Dynamical Systems with Averaging

    • M. I. Freidlin, A. D. Wentzell
    Pages 212-277

  10. Stability Under Random Perturbations

    • M. I. Freidlin, A. D. Wentzell
    Pages 278-293

  11. Sharpenings and Generalizations

    • M. I. Freidlin, A. D. Wentzell
    Pages 294-313

  12. Back Matter

    Pages 315-327
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Keywords

About this book

Asymptotical problems have always played an important role in probability theory. In classical probability theory dealing mainly with sequences of independent variables, theorems of the type of laws of large numbers, theorems of the type of the central limit theorem, and theorems on large deviations constitute a major part of all investigations. In recent years, when random processes have become the main subject of study, asymptotic investigations have continued to playa major role. We can say that in the theory of random processes such investigations play an even greater role than in classical probability theory, because it is apparently impossible to obtain simple exact formulas in problems connected with large classes of random processes. Asymptotical investigations in the theory of random processes include results of the types of both the laws of large numbers and the central limit theorem and, in the past decade, theorems on large deviations. Of course, all these problems have acquired new aspects and new interpretations in the theory of random processes.

Authors and Affiliations

  • VAAP Copyright Agency of the U.S.S.R., Moscow, USSR

    M. I. Freidlin, A. D. Wentzell

Bibliographic Information

  • Book Title: Random Perturbations of Dynamical Systems

  • Authors: M. I. Freidlin, A. D. Wentzell

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-1-4684-0176-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1984

  • eBook ISBN: 978-1-4684-0176-9Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: VIII, 328

  • Additional Information: Title of the original Russian edition: Fluktuacii v dinamiceskich sistemach pod dejstviem malych slucajnych vozmuscenij

  • Topics: Analysis

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