Course Archives Theoretical Statistics and Mathematics Unit | ||||||||
Course: Markov Chains Level: Postgraduate Time: Currently not offered |
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Syllabus Past Exams Syllabus: i) Finite State Markov Chains. Examples, Classification of States, Stationary Distribution. ii) Random walk on Finite Groups. Connection to electrical networks. Recurrence and Transience of Random walks. iii) Branching chain, progeny distribution and progeny generating function, extinc tion probability, geometric growth in the super-critical case. iv) Rates of convergence to stationarity, Dirichlet Form and Spectral gap methods, Some Coupling methods with applications, Cheegers inequality. v) Poisson Processes, Continuous time Markov Chains, Birth-and-death processes. Suggested Texts : (a) S. M. Ross, Stochastic processes, John Wiley (1996). (b) R. N. Bhattacharya and E. C. Waymire, Stochastic processes with applications. (c) E. Gine, R. Grimmett and L. Saloff-Coste, Lectures on probability theory and statistics, Springer-Verlag (1997). (d) L. Levine, Y. Peres and E. Wilmer: Markov Chains and Mixing times. (e) D. Aldous and J. A. Fill: Reversible Markov Chains and Random Walk on Graphs. Evaluation:
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Midterm
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