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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.


  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.


  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.