Lectures on Dynamics of Stochastic Systems

Lectures on Dynamics of Stochastic Systems

1st Edition - September 9, 2010

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  • Author: Valery Klyatskin
  • Hardcover ISBN: 9780123849663
  • eBook ISBN: 9780123849670

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Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. Models naturally render to statistical description, where random processes and fields express the input parameters and solutions. The fundamental problem of stochastic dynamics is to identify the essential characteristics of the system (its state and evolution), and relate those to the input parameters of the system and initial data. This book is a revised and more comprehensive version of Dynamics of Stochastic Systems. Part I provides an introduction to the topic. Part II is devoted to the general theory of statistical analysis of dynamic systems with fluctuating parameters described by differential and integral equations. Part III deals with the analysis of specific physical problems associated with coherent phenomena.

Key Features

  • A comprehensive update of Dynamics of Stochastic Systems
  • Develops mathematical tools of stochastic analysis and applies them to a wide range of physical models of particles, fluids and waves
  • Includes problems for the reader to solve


Researchers in physics (fluid dynamics, optics, acoustics, radiophysics), geosciences (ocean, atmosphere physics), applied mathematics (stochastic equations), applications (coherent phenomena). Senior and postgraduate students in different areas of physics, engineering and applied mathematics.

Table of Contents

  • Introduction

    Part I: Dynamical description of stochastic systems

    Lecture 1. Examples, basic problems, peculiar features of solutions

    Lecture 2. Solution dependence on problem type, medium parameters, and initial data

    Lecture 3. Indicator function and Liouville

    Part II: Statistical description of stochastic systems


    Lecture 4. Random quantities, processes, and fields

    Lecture 5. Correlation splitting

    Lecture 6. General approaches to analyzing stochastic systems

    Lecture 7. Stochastic equations with the Markovian fluctuations of


    Lecture 8. Approximation of Gaussian random field delta-correlated

    in time

    Lecture 9. Methods for solving and analyzing the Fokker-Planck


    Lecture 10. Some other approximate approaches to the problems of

    statistical hydrodynamics

    Part III: Examples of coherent phenomena in stochastic dynamic systems 269

    Lecture 11. Passive tracer clustering and diffusion in random hydrodynamic and magnetohydrodynamic flows

    Lecture 12. Wave localization in randomly layered media

    Lecture 13. Caustic structure of wavefield in random media


Product details

  • No. of pages: 410
  • Language: English
  • Copyright: © Elsevier 2010
  • Published: September 9, 2010
  • Imprint: Elsevier
  • Hardcover ISBN: 9780123849663
  • eBook ISBN: 9780123849670

About the Author

Valery Klyatskin

Born in 1940 in Moscow, USSR, Valery I. Klyatskin received his secondary education at school in Tbilisi, Georgia, finishing in 1957. Seven years later he graduated from Moscow Institute of Physics and Technology (FIZTEX), whereupon he took up postgraduate studies at the Institute of Atmospheric Physics USSR Academy of Sciences, Moscow gaining the degree of Candidate of Physical and Mathematical Sciences (Ph.D) in 1968. He then continued at the Institute as a researcher, until 1978, when he was appointed as Head of the Wave Process Department at the Pacific Oceanological Institute of the USSR Academy of Sciences, based in Vladivostok. In 1992 Valery I. Klyatskin returned to Institute of Atmospheric Physics Russian Academy of Sciences, Moscow when he was appointed to his present position as Chief Scientist. At the same time he is Chief Scientific Consultant of Pacific Oceanological Institute Russian Academy of Sciences, Vladivostok. In 1977 he obtained a doctorate in Physical and Mathematical Sciences and in 1988 became Research Professor of Theoretical and Mathematical Physics, Russian Academy of Science.

Affiliations and Expertise

Russian Academy of Science, Russia

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