Course Archives Theoretical Statistics and Mathematics Unit
Course:
Introduction to Stochastic Processes
Level:
Undergraduate
Time:
Currently not 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).
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Past Exams
Midterm
24.pdf
Semestral
24.pdf
Supplementary and Back Paper
24.pdf
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