DEPARTMENT OF MATHEMATICS

MTL 794 (3-0-0) Advanced Probability Theory

I Semester 2021-2022

Lecture Classes (Slot AD): Tuesday and Friday between 3:30 PM and 4:50 PM online

Pre-requisite: MTL106 or MTL601

Course Contents

Notions of Stochastic Convergence and Related Convergence Theorems, Uniform Integrability, Weak and Strong Laws of Large Numbers, Speed of Convergence in the Strong Laws of Large Numbers, Martingales, Processes, Filtrations, Stopping Times, Discrete Stochastic Integral, Martingale Convergence Theorems and Their Applications, Levy’s Continuity Theorem and Various Versions of Central Limit Theorem, Markov Chains, Discrete Markov Chains, Convergence of Markov Chains, Applications of Probability Theory to Fourier Series-Examples.

Main Text Books

Probability Theory, S R S Varadhan, AMS Publications, 2001.

Reference Books

1. S R S Varadhan, Stochastic Processes, Courant Lecture Notes, 2007.

2. Williams, D. (1991): Probability with Martingales. Cambridge University Press

3. Kallenberg, O. (2002). Foundations of modern probability.

4. Billingsley, P. (2008). Probability and measure. John Wiley & Sons

5. Jacod, J., & Protter, P. E. (2003). Probability essentials. Springer

6. Kai Lai Chung. A Course in Probability Theory. Academic Press, second edition, 1974.

This page maintained by Dr. S. Dharmaraja mailto:dharmar@maths.iitd.ac.in and last updated Tuesday, Aug. 03, 2021.