Q2515053
type: Item
instance of: scholarly article
title: Stochastic equations: theory and applications in acoustics, hydrodynamics, magnetohydrodynamics, and radiophysics. Volume 2. Coherent phenomena in stochastic dynamic systems. Translated from the Russian by A. Vinogradov
zbMATH Open document ID: 1333.60007
DOI: 10.1007/978-3-319-07590-7
published in: Understanding Complex Systems
publication date: 2015-02-09T00:00:00Z
review text: In the present second volume, the methods developed in the first volume are used in the theory of coherent phenomena occurring in stochastic dynamic systems with probability one, that is, clustering of particles and passive scalar tracer field (density field) in a random velocity field, passive vector tracer field (magnetic field) in a random velocity field, dynamic localization of plane waves in layered random media, propagation of monochromatic waves in random media, and formation of caustic structures in different-nature wavefields propagating in multidimensional random media (under the assumption that wave propagation is described in terms of a scalar parabolic equation). In the preface to this volume, the author says: ``It would be physically impossible to give an exhaustive bibliography'' -- and he refers nearly only to his own papers, in both volumes. They were cited in the past, but his recent books are not cited. Probably the reason is the style: no generally accepted terms and forms of presentation for stochastic differential equations for Markov processes are applied; instead of referring to well-known books with a description of Wiener processes, the author gives it in a nonstandard way [Vol. 1, p.\,10] and does not refer at all to mathematical textbooks or monographs with finely described models and conceptions of stochastic differential equations. For a review of the first volume, see [Zbl 1333.60006].
reviewed by: Svetlana Anulova
Mathematics Subject Classification ID: 60-02
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60H20
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 37H10
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60K37
Mathematics Subject Classification ID: 82C31
Mathematics Subject Classification ID: 35Q84
Mathematics Subject Classification ID: 76W05
zbMATH DE Number: 6399802
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: stochastic integral equations
zbMATH Keywords: random processes
zbMATH Keywords: stochastic dynamical systems
zbMATH Keywords: Markov fluctuations
zbMATH Keywords: Fokker-Planck equation
zbMATH Keywords: asymptotic methods
zbMATH Keywords: approximate methods
zbMATH Keywords: acoustics
zbMATH Keywords: hydrodynamics
zbMATH Keywords: magnetohydrodynamics
author: V. I. Klyatskin
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-07590-7
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label: Stochastic equations: theory and applications in acoustics, hydrodynamics, magnetohydrodynamics, and radiophysics. Volume 2. Coherent phenomena in stochastic dynamic systems. Translated from the Russian by A. Vinogradov
description: scientific article