# Course

Course No:
M472
Credit:
4
Prerequisites:
M206
Approval:
2014
UG-Elective
PG-Core
Syllabus:
Probability spaces, Random Variables, Independence, Zero-One Laws, Expectation, Product spaces and Fubini’s theorem, Convergence concepts, Law of large numbers, Kolmogorov three-series theorem, Levy-Cramer Continuity theorem, CLT for i.i.d. components, Infinite Products of probability measures, Kolmogorov’s Consistency theorem, Conditional expectation, Discrete parameter martingales with applications.
Reference Books:
1. A. Gut, “Probability: A Graduate Course”, Springer Texts in Statistics, Springer, 2013.
2. K. L. Chung, “A Course in Probability Theory”, Academic Press, 2001.
3. S. I. Resnick, “A Probability Path”, Birkh ̈auser, 1999.
4. P. Billingsley, “Probability and Measure”, Wiley Series in Probability and Statistics, John Wiley & Sons, 2012.
5. J. Jacod, P. Protter, “Probability Essentials”, Universitext, Springer-Verlag, 2003