Stochastic equations: theory and applications in acoustics, hydrodynamics, magnetohydrodynamics, and radiophysics. Volume 1. Basic concepts, exact results, and asymptotic approximations. Translated from the Russian by A. Vinogradov (Q2515052)

In the first of the two volumes of this work, general methods for stochastic equations are developed. The author considers a statistical theory of dynamic and wave systems with fluctuating parameters. These systems can be described by ordinary differential equations, partial differential equations, integro-differential equations, integral equations, and boundary-value problems (in wave problems). The considered dynamic systems are mainly with fluctuating parameters being Gaussian random processes (fields), although the presented theory is valid also for general fluctuating parameters. The physical systems in the book are mainly taken from statistical hydrodynamics, statistical radiophysics and acoustics (the author's earlier research). However, similar problems and solution techniques occur in plasma physics, solid-state physics, and magnetohydrodynamics. For Gaussian fluctuating parameters, the functional method devised by Novikov in turbulence theory is applied; this method was developed by the author for general dynamic systems and fluctuating parameters of arbitrary nature. The Markov property of the solutions and equations for probability densities (Fokker-Planck, Kolmogorov-Feller type) are established. For a review of the second volume, see [Zbl 1333.60007].