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Lectures on Dynamics of Stochastic Systems
ID: 173398
Valery Klyatskin
Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come from either the typical forces, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. Models naturally render to statistical description. The fundamental problem of stochastic dynamics is to identify the system and its data.
This book is a revised and comprehensive version of Dynamics of Stochastic Systems . Part I is an introduction to the topic. Part II is devoted to the general theory of differential and integral equations. Part III deals with the physical problem 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
173398
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Valery Klyatskin