Prerequisites: IE 611 or equivalent and Instructor's consent.
Course contents
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Construction of Probability Measure, Integration, Convergence theorems, Law of large numbers and Central limit theorem. Lp spaces and Conditional expectation.
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Martingales : Super and Sub martingales, Doob's inequalities, Martingale convergence theorems.
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Analysis of M/G/1 and GI/M/1 queues. Derivation of Little's law and PASTA.
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Markov chains and stability (general state space, e.g., Rn): Introduction, \psi-irreducibility, Small sets, Transience and Recurrence. Drift criterion, SLLN, CLT.
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Random Walk Models, Analysis of G/G/1 queues using Ladder chains.
References
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Jean Jacod, Philip E. Protter, 'Probability Essentials', Springer, 2003.
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Sean Meyn and Richard L. Tweedie, 'Markov Chains and Stochastic Stability', Springer-Verlag London Ltd, 1993.
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P. Billingsley, 'Probability and Measure', third ed., Wiley-Interscience, New York, 1995.
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R. W. Wolff, 'Stochastic modelling and the theory of queues', Prentice Hall Inc., Englewood Cliffs, 1989.
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Relevant Research papers.