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.
Author(s): Valery I. Klyatskin (auth.)
Series: Understanding Complex Systems
Edition: 1
Publisher: Springer International Publishing
Year: 2015
Language: English
Pages: 418
Tags: Complexity; Socio- and Econophysics, Population and Evolutionary Models; Dynamical Systems and Ergodic Theory; Engineering Fluid Dynamics
Front Matter....Pages 1-16
Front Matter....Pages 1-1
Examples, Basic Problems, Peculiar Features of Solutions....Pages 3-80
Solution Dependence on Problem Type, Medium Parameters, and Initial Data....Pages 81-93
Indicator Function and Liouville Equation....Pages 95-114
Front Matter....Pages 115-115
Random Quantities and Their Characteristics....Pages 117-123
Random Processes and Their Characteristics....Pages 125-154
Random Fields....Pages 155-164
Correlation Splitting....Pages 165-189
Front Matter....Pages 191-191
General Approaches to Analyzing Stochastic Dynamic Systems....Pages 193-260
Stochastic Equations with the Markovian Fluctuations of Parameters....Pages 261-301
Front Matter....Pages 303-303
Gaussian Random Field Delta-Correlated in Time (Ordinary Differential Equations)....Pages 305-340
Methods for Solving and Analyzing the Fokker-Planck Equation....Pages 341-375
Diffusion and Higher Approximations....Pages 377-389
Some Other Approximate Approaches to the Problems of Statistical Hydrodynamics....Pages 391-405
Back Matter....Pages 407-417
