Lectures on Dynamics of Stochastic Systems

1st Edition

Print ISBN: 9780323165167
eBook ISBN: 9780123849670
Imprint: Elsevier
Published Date: 9th September 2010
Page Count: 410
77.95 + applicable tax
47.99 + applicable tax
59.95 + applicable tax
Compatible Not compatible
VitalSource PC, Mac, iPhone & iPad Amazon Kindle eReader
ePub & PDF Apple & PC desktop. Mobile devices (Apple & Android) Amazon Kindle eReader
Mobi Amazon Kindle eReader Anything else

Institutional Access


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


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



No. of pages:
© Elsevier 2011
eBook ISBN:
Hardcover ISBN:
Paperback ISBN:


"...an extensively revised and more detailed version of the author's earlier book...a statistical description and analysis of dynamic systems that occur in physics and related areas."--MathSciNet, Lectures on Dynamics of Stochastic Systems

"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