Dynamics Of Stochastic Systems

Fluctuating parameters appear in a variety of physical systems and phenomena.They typically come either as random forcessources or advecting velocitiesor media ... » 

Fluctuating parameters appear in a variety of physical systems and phenomena.They typically come either as random forcessources or advecting velocitiesor media material parameters like refraction index conductivitydiffusivity etc. The well known example of Brownian particle suspended influid and subjected to random molecular bombardment laid the foundation formodern stochastic calculus and statistical physics. Other important examplesinclude turbulent transport and diffusion of particletracers pollutants orcontinuous densities oil slicks wave propagation and scattering inrandomly inhomogeneous media for instance light or sound propagating in theturbulent atmosphere.Such models naturally render to statistical description where the inputparameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essentialcharacteristics of system its state and evolution and relate those to theinput parameters of the system and initial data.This raises a host of challenging mathematical issues. One could rarely solvesuch systems exactly or approximately in a closed analytic form and theirsolutions depend in a complicated implicit manner on the initialboundary dataforcing and systems media parameters . In mathematical terms such solutionbecomes a complicated nonlinear functional of random fields and processes.Part I gives mathematical formulation for the basic physical models oftransport diffusion propagation and develops some analytic tools.Part II sets up and applies the techniques of variational calculus andstochastic analysis like FokkerPlankequation to those models to produceexact or approximate solutions or in worst case numeric procedures. Theexposition is motivated and demonstrated with numerous examples.Part III takes up issues for the coherent phenomena in stochastic dynamicalsystems described by or «