Lectures on Dynamics of Stochastic Systems book cover

Lectures on Dynamics of Stochastic Systems

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.

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.

Hardbound, 410 Pages

Published: September 2010

Imprint: Elsevier

ISBN: 978-0-12-384966-3


  • "Taking into account opinions and wishes of readers about both the style of the text and the choice of specific problems, the aim of the book at this edition is simply to present the subject of its title sourced from the series of lectures that the author gave to scientific associates at the Institute of Calculus Mathematics, Russian Academy of Sciences. Each lecture is appended with problems for readers."--Zentralblatt MATH 2012-1233-93001


  • 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



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