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Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 1

Basic Concepts, Exact Results, and Asymptotic Approximations

  • Valery I.¬†Klyatskin

Part of the Understanding Complex Systems book series (UCS)

Table of contents

  1. Front Matter
    Pages 1-16
  2. Dynamical Description of Stochastic Systems

    1. Front Matter
      Pages 1-1
    2. Valery I. Klyatskin
      Pages 95-114
  3. Random Quantities, Processes, and Fields

    1. Front Matter
      Pages 115-115
    2. Valery I. Klyatskin
      Pages 117-123
    3. Valery I. Klyatskin
      Pages 125-154
    4. Valery I. Klyatskin
      Pages 155-164
    5. Valery I. Klyatskin
      Pages 165-189
  4. Stochastic Equations

    1. Front Matter
      Pages 191-191
  5. Asymptotic and Approximate Methods for Analyzing Stochastic Equations

  6. Back Matter
    Pages 407-417

About this book

Introduction

This monograph set presents a consistent and self-contained framework of stochastic dynamic systems with maximal possible completeness. Volume 1 presents the basic concepts, exact results, and asymptotic approximations of the theory of stochastic equations on the basis of the developed functional approach. This approach offers a possibility of both obtaining exact solutions to stochastic problems for a number of models of fluctuating parameters and constructing various asymptotic buildings. Ideas of statistical topography are used to discuss general issues of generating coherent structures from chaos with probability one, i.e., almost in every individual realization of random parameters. The general theory is illustrated with certain problems and applications of stochastic mathematical physics in various fields such as mechanics, hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics.

 

Keywords

Complex Systems Stochastic Dynamic Systems Stochastic Dynamics Stochastic Equations

Authors and affiliations

  • Valery I.¬†Klyatskin
    • 1
  1. 1.Russian Academy of SciencesA.M. Obukhov Institute of Atmospheric PhysicsMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-07587-7
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-07586-0
  • Online ISBN 978-3-319-07587-7
  • Series Print ISSN 1860-0832
  • Series Online ISSN 1860-0840
  • Buy this book on publisher's site