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September 23, 2023

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Description

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)

Course Curriculum

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

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