Lectures on Dynamics of Stochastic Systems

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