Stochastics processes. Stochastics variables, random events, multivariate distributions, statistical distributions, the correlation functions, Markov processes, the Chapman-Kolmogorov equation, Markov chains.
The master equation. Derivation and examples, the class of W-matrices, appliance in closed and isolated physical systems, the principle of detailed balance, expansion in eigenfunctions, the macroscopic equation, the adjoint equation, one-step processes - examples and solutions, random walk, nonlinear one-step processes.
The Fokker-Planck equation. Derivation and examples, Brownian motion, the Rayleigh particle, application to one-step processes, the multivariate Fokker-Planck equation, Kramers' equation.
The Langevin approach. Langevin treatment of Brownian motion, applications, relation to Fokker-Planck equation, Ito-Stratonovich dilemma, non-Gaussian white noise, colored noise.
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