Lectures on Dynamics of Stochastic Systems

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 gaining the degree of Candidate of Physical and Mathematical Sciences (Ph.D) in 1968. He then continued at the Institute as a researcher, until 1978, when he was appointed as Head of the Wave Process Department at the Pacific Oceanological Institute of the USSR Academy of Sciences, based in Vladivostok. In 1992 Valery I. Klyatskin returned to Institute of Atmospheric Physics Russian Academy of Sciences, Moscow when he was appointed to his present position as Chief Scientist. At the same time he is Chief Scientific Consultant of Pacific Oceanological Institute Russian Academy of Sciences, Vladivostok. In 1977 he obtained a doctorate in Physical and Mathematical Sciences and in 1988 became Research Professor of Theoretical and Mathematical Physics, Russian Academy of Science.

• 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 dataLecture 3. Indicator function and Liouville Part II: Statistical description of stochastic systemsLecture 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 ofparameters Lecture 8. Approximation of Gaussian random field delta-correlatedin time Lecture 9. Methods for solving and analyzing the Fokker-Planckequation Lecture 10. Some other approximate approaches to the problems ofstatistical hydrodynamics Part III: Examples of coherent phenomena in stochastic dynamic systems 269Lecture 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 mediaBibliography

"...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