Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 1, 2015 Basic Concepts, Exact Results, and Asymptotic Approximations Understanding Complex Systems Series

This monograph set presents a consistent and self-contained framework of stochastic dynamic systems with maximal possible completeness. Volume 1 presents the basic concepts, exact results, and asymptotic approximations of the theory of stochastic equations on the basis of the developed functional approach. This approach offers a possibility of both obtaining exact solutions to stochastic problems for a number of models of fluctuating parameters and constructing various asymptotic buildings. Ideas of statistical topography are used to discuss general issues of generating coherent structures from chaos with probability one, i.e., almost in every individual realization of random parameters. The general theory is illustrated with certain problems and applications of stochastic mathematical physics in various fields such as mechanics, hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics.

Dynamical description of stochastic systems.- Random quantities, processes, and fields.- Stochastic equations.- Asymptotic methods for analyzing stochastic equations.

Presents a consistent framework of stochastic dynamic systems with maximal possible completeness

The present Volume 2 presents Coherent Phenomena in Stochastic Dynamic Systems

Studies specific problems of the stochastic structure formation in random media not published elsewhere before

With illustrative applications from acoustics, hydrodynamics, magnetohydrodynamics, wave dynamics, and radiophysics