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Physical Applications of Stochastic Processes

Physical Applications of Stochastic Processes. Instructor: Professor V. Balakrishnan, Department of Physics, IIT Madras. 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. (from nptel.ac.in)

Discrete Probability Distributions


Lecture 01 - Discrete Probability Distributions (Part 1)
Lecture 02 - Discrete Probability Distributions (Part 2)
Lecture 03 - Continuous Random Variables
Lecture 04 - Central Limit Theorem
Lecture 05 - Stable Distributions
Lecture 06 - Stochastic Processes
Lecture 07 - Markov Processes (Part 1)
Lecture 08 - Markov Processes (Part 2)
Lecture 09 - Markov Processes (Part 3)
Lecture 10 - Birth-and-Death Processes
Lecture 11 - Continuous Markov Processes
Lecture 12 - Langevin Dynamics (Part 1)
Lecture 13 - Langevin Dynamics (Part 2)
Lecture 14 - Langevin Dynamics (Part 3)
Lecture 15 - Langevin Dynamics (Part 4)
Lecture 16 - Ito and Fokker-Planck Equations for Diffusion Processes
Lecture 17 - Level-crossing Statistics of a Continuous Random Process
Lecture 18 - Diffusion of a Charged Particle in a Magnetic Field
Lecture 19 - Power Spectrum of Noise
Lecture 20 - Elements of Linear Response Theory
Lecture 21 - Random Pulse Sequences
Lecture 22 - Dichotomous Diffusion
Lecture 23 - First Passage Time (Part 1)
Lecture 24 - First Passage Time (Part 2)
Lecture 25 - First Passage and Recurrence in Markov Chains
Lecture 26 - Recurrent and Transient Random Walks
Lecture 27 - Non-Markovian Random Walks
Lecture 28 - Statistical Aspects of Deterministic Dynamics (Part 1)
Lecture 29 - Statistical Aspects of Deterministic Dynamics (Part 2)

References
Physical Applications of Stochastic Processes
Instructor: Professor V. Balakrishnan, Department of Physics, IIT Madras. Probability and statistics, Stochastic processes, Continuous Markov processes, Stochastic differential equations, Random walks, and Randomness in deterministic dynamics.