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MA 262: Introduction to Stochastic Processes
Credits: 3:0
Discrete parameter Markov Chains: Chapman-Kolmogorov equations, Classification of states, Limit Theorems, Examples: Random Walks, Gambler’s Ruin, Branching processes. Time reversible Markov chains. Simulations and MCMC (16 lectures)
Poisson processes, Definitions, and properties: interarrival and waiting time distributions, superposition and thinning, Nonhomogeneous Poisson process, Compound Poisson process. Simulation. (5 lectures)
Continuous time Markov Chains: Definition, Birth-Death processes, Kolmogorov backward and forward equations, Limiting probabilities, Time reversibility. Queueing Theory, Simulation. (10 lectures)
Renewal Theory. (3 lectures)
Brownian Motion. (6 lectures).
Suggested books and references:
Karlin and Taylor,
A first course in Stochastic Processes
, Academic Press; 2nd edition, 1975.
Sheldon Ross,
Stochastic Processes
, Wiley; 2nd edition, 2008.
Bhattacharya and Waymire,
Stochastic Processes and Applications
, Society for Industrial and Applied Mathematics, 2009.
All Courses
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+91 (80) 2293 2711, +91 (80) 2293 2265 ;
E-mail:
chair.math[at]iisc[dot]ac[dot]in
Last updated: 20 Mar 2023