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.
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.

Physical Applications of Stochastic Processes
Prof. Balakrishnan explaining Markov Processes in Lecture 7.
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Video Lectures & Study Materials

Visit the official course website for more study materials:

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


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