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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.

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

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"The book represents a comprehensive and very well-written study of stochastic equations and their applications to acoustics, hydrodynamics, and other branches of physics. ... The book may be recommended to all interested in the subject; it is really a pleasant read! The book may be also recommended as a textbook for graduate students in both stochastic analysis and diverse areas of applied mathematics." (B. Belinskiy, Mathematical Reviews, August, 2015)

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