IIT Madras Course , Prof. V. Balakrishnan

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IIT Madras Course , Prof. V. Balakrishnan

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. 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 - 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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3.2 (46 Ratings)

Physical Applications of Stochastic Processes by Prof. V. Balakrishnan,Department of Physics,IIT Madras.For more details on NPTEL visit httpnptel.ac.in

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- 1.Discrete probability distributions (Part 1)
- 2.Discrete probability distributions (Part 2)
- 3.Continuous random variables
- 4.Central Limit Theorem
- 5.Stable distributions
- 6.Stochastic processes
- 7.Markov processes (Part 1)
- 8.Markov processes (Part 2)
- 9.Markov processes (Part 3)
- 10.Birth-and-death processes
- 11.Continous Markov processes
- 12.Langevin dynamics (Part 1)
- 13.Langevin dynamics (Part 2)
- 14.Langevin dynamics (Part 3)
- 15.Langevin dynamics (Part 4)
- 16.Ito^ and Fokker-Planck equations for diffusion processes
- 17.Level-crossing statistics of a continuous random process
- 18.Diffusion of a charged particle in a magnetic field
- 19.Power spectrum of noise
- 20.Elements of linear response theory
- 21.Random pulse sequences
- 22.Dichotomous diffusion
- 23.First passage time (Part 1)
- 24.First passage time (Part 2)
- 25.First passage and recurrence in Markov chains
- 26.Recurrent and transient random walks
- 27.Non-Markovian random walks
- 28.Statistical aspects of deterministic dynamics (Part 1)
- 29.Statistical aspects of deterministic dynamics (Part 2)

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