Lectures on Dynamics of Stochastic Systems

<p>Introduction </p> <p>Part I: Dynamical description of stochastic systems </p> <p>Lecture 1. Examples, basic problems, peculiar features of solutions </p> <p>Lecture 2. Solution dependence on problem type, medium parameters, and initial data</p> <p>Lecture 3. Indicator function and Liouville </p> <p>Part II: Statistical description of stochastic systems</p> <p>Lecture 4. Random quantities, processes, and fields </p> <p>Lecture 5. Correlation splitting </p> <p>Lecture 6. General approaches to analyzing stochastic systems </p> <p>Lecture 7. Stochastic equations with the Markovian fluctuations of</p> <p>parameters </p> <p>Lecture 8. Approximation of Gaussian random field delta-correlated</p> <p>in time </p> <p>Lecture 9. Methods for solving and analyzing the Fokker-Planck</p> <p>equation </p> <p>Lecture 10. Some other approximate approaches to the problems of</p> <p>statistical hydrodynamics </p> <p>Part III: Examples of coherent phenomena in stochastic dynamic systems 269</p> <p>Lecture 11. Passive tracer clustering and diffusion in random hydrodynamic and magnetohydrodynamic flows </p> <p>Lecture 12. Wave localization in randomly layered media </p> <p>Lecture 13. Caustic structure of wavefield in random media</p> <p>Bibliography</p>