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Lectures on Dynamics of Stochastic Systems
Reviews the latest developments in stochastic dynamic systems covering areas such as acoustics, hydrodynamics, magneto-hydrodynamics, radiophysics, theoretical and mathematical physics and applied mathematics
Valery I. Klyatskin (Author)
9780123849663, Elsevier Science
Hardback, published 9 September 2010
410 pages
22.9 x 15.1 x 2.7 cm, 0.77 kg
"...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
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.
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
