Advanced Probability

Code: MA684 | L-T-P-C: 3-0-0-6

MA684 ADVANCED PROBABILITY L-T-P-C [3-0-0-6] Pre requisites: MA 590 or equivalent

Measure theoretic formulation of probability; Random variables, Distributions, Expectations, Modes of convergence; Laws of large numbers:the weak and strong laws; Characteristic functions, Convergence in distribution, Central limit theorems; Markov chains, Random walks, Poisson process; Conditional expectations; Discrete parameter martingales,Convergence theorems for martingales; Brownian motion, Strong Markov property, Introduction to sample path properties.

Texts:

1. J.B. Walsh, Knowing the Odds: An Introduction to Probability, American Mathematical Society, 2012.
2. K. B. Athreya and S. N. Lahiri, Probability Theory, TRIM series, 2006.

References:

1. P. Billingsley, Probability and Measure, Wiley India, 3rd Edn., 2008.
2. R. Durrett, Probability: Theory and Examples, Cambridge University Press, 4th Edn.,2010.
3. O. Kallenberg, Foundations of Modern Probability, Springer, 2nd Edn., 2002.