Martingales and Brownian Motion

Code: MA685 | L-T-P-C: 3-0-0-6

Prerequisites: MA590 or equivalent

Review of measure theoretic formulation of probability; Conditional expectations, Martingales, Convergence, Uniform integrability, Applications; Brownian motion, Construction of Brownian motion, Stopping times and Strong Markov property, Zero set of Brownian motion, Reflection principle, Recurrence and hitting properties, Path irregularity, Skorokhod embedding, Glimpses of a few advanced topics: processes derived from Brownian motion and the Wiener integral.

Text:

1. J. B. Walsh, Knowing the Odds: An Introduction to Probability, American Mathematical Society, 2012.

References:

1. R. Durrett. Probability: Theory and Examples, 4th Edn, Cambridge University Press, 2010.
2. O. Kallenberg, Foundations of Modern Probability, 2nd Edn, Springer, 2002.
3. P. Mörs and Y. Peres, Brownian motion, Cambridge University Press, 2010.
4. D. Williams, Probability with Martingales, Cambridge University Press, 1991.