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Lectures on Dynamics of Stochastic Systems
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  • Lectures on Dynamics of Stochastic Systems
ID: 173398
Valery Klyatskin
Wycofany

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 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



  • A comprehensive update of Dynamics of Stochastic Systems

  • Develops mathematical tools of stochastic analysis and applies them to a wide range of physical models of particles, fluids and waves

  • Includes problems for the reader to solve


    • 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

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