Abstract

Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. Models naturally render to statistical description, where random processes and fields express the input parameters and solutions. The fundamental problem of stochastic dynamics is to identify the essential characteristics of the system (its state and evolution), and relate those to the input parameters of the system and initial data.

This book is a revised and more comprehensive version of Dynamics of Stochastic Systems. Part I provides an introduction to the topic. Part II is devoted to the general theory of statistical analysis of dynamic systems with fluctuating parameters described by differential and integral equations. Part III deals with the analysis of specific physical problems associated with coherent phenomena.

• A comprehensive update of Dynamics of Stochastic Systems
• Develops mathematical tools of stochastic analysis and applies them to a wide range of physical models of particles, fluids and waves
• Includes problems for the reader to solve

"...an extensively revised and more detailed version of the author's earlier book...a statistical description and analysis of dynamic systems that occur in physics and related areas."--MathSciNet, Lectures on Dynamics of Stochastic Systems

"Taking into account opinions and wishes of readers about both the style of the text and the choice of specific problems, the aim of the book at this edition is simply to present the subject of its title sourced from the series of lectures that the author gave to scientific associates at the Institute of Calculus Mathematics, Russian Academy of Sciences. Each lecture is appended with problems for readers."--Zentralblatt MATH 2012-1233-93001