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Physical Applications of Stochastic Processes

Course Description

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.

Course Objective

This course covers following topics:-

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.  Campbell's Theorem,  Carson's 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.

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