| Introduction to Stochastic Processes |
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
Poisson processes, Definitions, and properties: interarrival and waiting time distributions,
superposition and thinning, Nonhomogeneous Poisson process, Compound Poisson process. Simulation.
Continuous time Markov Chains: Definition, Birth-Death processes, Kolmogorov backward and forward equations,
Limiting probabilities, Time reversibility. Queueing Theory, Simulation.
Renewal Theory
Brownian Motion |
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Prof Arvind Ayyer |