Course Archives Theoretical Statistics and Mathematics Unit

Course: Introduction to Stochastic Processes Instructor: Yogeshwaran D Room: G23 Level: Undergraduate Time: Currently offered

Syllabus Past Exams Syllabus: DISCRETE-TIME MARTINGALES: Optional Stopping theorem, Martingale convergence theorem, Doobs inequality and convergence. BRANCHING PROCESSES: Model definition. Connection with martingales. Probability of survival. Mean and variance of number of individuals. DISCRETE-TIME MARKOV CHAINS: Classification of states, Stationary distribution, reversibility and convergence. Random walks and electrical networks. Collision and recurrence. BASIC PROBABILISTIC INEQUALITIES AND APPLICATIONS: First and Second Moment methods. Applications to Longest increasing subsequences, Random k-Sat problem and connectivity threshold for Erdos-Renyi graphs. Chernoff bounds and Johnson-Lindenstrauss lemma. Reference Texts: (a) N. Lanchier: Stochastic Modelling. (b) W. Feller: Introduction to Probability: Theory and Applications - Vol. I and II.. (c) L. Levine, Y. Peres and E. Wilmer: Markov chains and mixing times. (d) Sheldon Ross: Probability Models. (e) Santosh S. Venkatesh: Theory of Probability - Explorations and Applications. (f) R. Meester: A Natural Introduction to Probability Theory. (g) S. R. Athreya and V. S. Sunder: Measure and Probability. (h) Sebastien Roch: Modern Discrete Probability: A toolkit. (Notes). Evaluation: Mid-term 15 marks Assignment 35 marks Final Exam 50 marks Total 100 marks Top of the page Past Exams

Midterm 24.pdf 25.pdf Semestral 24.pdf Supplementary and Back Paper Top of the page

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