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.
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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e-book enables you to access interactive reading material to strengthen the skills learned in the sessions.
Online Lab enables you to practice the application of concepts you have learnt in the sessions in the virtual environment.
Tutorials enables you to get easy learning with clear, crisp, and to-the-point content on a wide range of technical and non-technical subjects without any preconditions and impediments.