http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Lectures on dynamics of stochastic systems
Kli︠a︡t︠s︡kin, V. I. (Valeriĭ Isaakovich)
1 online resource (xiv, 396 pages) : illustrations.
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.
Part I: Dynamical description of stochastic systems -- 1. Examples, basic problems, peculiar features of solutions -- 2. Solution dependence on problem type, medium parameters, and initial data -- 3. Indicator function and Liouville -- Part II: Statistical description of stochastic systems -- 4. Random quantities, processes, and fields -- 5. Correlation splitting -- 6. General approaches to analyzing stochastic systems -- 7. Stochastic equations with the Markovian fluctuations of -- parameters -- 8. Approximation of Gaussian random field delta-correlated in time -- 9. Methods for solving and analyzing the Fokker-Planck equation -- 10. Some other approximate approaches to the problems of statistical hydrodynamics -- Part III: Examples of coherent phenomena in stochastic dynamic systems -- 11. Passive tracer clustering and diffusion in random hydrodynamic and magnetohydrodynamic flows -- 12. Wave localization in randomly layered media -- 13. Caustic structure of wavefield in random media.
edited by Valery I. Klyatskin ; translated from Russian by A. Vinogradov.