Lectures on Dynamics of Stochastic Systems

Hardcover | September 10, 2010

byValery I. KlyatskinEditorValery I. Klyatskin

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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. 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

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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 th...

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 ...

other books by Valery I. Klyatskin

Dynamics Of Stochastic Systems
Dynamics Of Stochastic Systems

Paperback|May 20 2005

$101.34 online$106.50list price
Format:HardcoverDimensions:410 pages, 9 × 6 × 0.98 inPublished:September 10, 2010Publisher:Elsevier Science & TechLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0123849667

ISBN - 13:9780123849663

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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

parameters

Lecture 8. Approximation of Gaussian random field delta-correlated

in time

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

equation

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

Bibliography

Editorial Reviews

"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