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Physics  Physical Applications of Stochastic Processes
Title: Physical Applications of Stochastic Processes
Department: Physics
Author: Prof. V. Balakrishnan
University: IIT Madras
Type: WebLink
Abstract: Probability and statistics: Joint and conditional probabilities and densities. Moments, cumulants, generating functions, characteristic function. Binomial, Poisson, Gaussian distributions. Stable distributions, limit theorems, diffusion limit of random flights. Infinitely divisible distributions.
Stochastic processes: Discrete and continuous random processes. Joint and conditional probability distributions. Autocorrelation function. Markov chains. Discrete Markov processes, master equation. Poisson process, birth'and'death processes. Jump processes. Correlation functions, power spectra. Campbells Theorem, Carsons Theorem. Thermal, shot, Barkhausen and 1/f noise.
Continuous Markov processes: Chapman'Kolmogorov equation, transition rate, Kramers'Moyal expansion. Fokker'Planck equation, backward Kolmogorov equation, first passage and exit time problems. Level'crossing statistics.
Stochastic differential equations: Langevin equation, diffusion processes, Brownian motion, role of dimensionality, fractal properties.
Random walks: Markovian random walks. Random walks and electrical networks, random walks in biology. Levy flights. Self'avoiding walks and polymer dynamics. Random walks on fractals. Non'Markov continuous time random walks.
Randomness in deterministic dynamics: Coarse'grained dynamics, Markov and generating partitions, recurrence statistics.
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