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 --- marks Assignment 50 marks Final Exam 50 marks Total 100 marks Top of the page Past Exams

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

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