Coherent phenomena in stochastic dynamical systems

Abstract

Basic ideas of the statistical topography of random processes and fields are presented, which are used in the analysis of coherent phenomena in simple dynamical systems. Such phenomena take place with probability one, and provide links between individual realizations and statistical characteristics of systems at large. We confine ourselves to several examples: transfer phenomena in singular dynamic systems under the action of random forces; dynamic localization of plane waves in randomly stratified media; clustering of randomly advected passive tracers; and formation of caustic structures for wave fields in randomly inhomogeneous media. All these phenomena are studied based on the analysis of one-point (space-time) probability distribution functions.