MA 262: Introduction to Stochastic Processes

Credits: 3:0

  1. 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)
  2. Poisson processes, Definitions, and properties: interarrival and waiting time distributions, superposition and thinning, Nonhomogeneous Poisson process, Compound Poisson process. Simulation. (5 lectures)
  3. Continuous time Markov Chains: Definition, Birth-Death processes, Kolmogorov backward and forward equations, Limiting probabilities, Time reversibility. Queueing Theory, Simulation. (10 lectures)
  4. Renewal Theory. (3 lectures)
  5. Brownian Motion. (6 lectures).

Suggested books and references:

  1. Karlin and Taylor, A first course in Stochastic Processes, Academic Press; 2nd edition, 1975.
  2. Sheldon Ross, Stochastic Processes, Wiley; 2nd edition, 2008.
  3. Bhattacharya and Waymire, Stochastic Processes and Applications, Society for Industrial and Applied Mathematics, 2009.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 13 Jun 2024