Department of Mathematics

INDIAN INSTITUTE OF SCIENCE

MA 368: Topics in Probability and Stochastic Processes

Credits: 3:0

Prerequisite courses: MA361

Discrete parameter martingales: Conditional expectation. Optional sampling theorems. Doob’s inequalities. Martingale convergence theorems. Applications.

Brownian motion. Construction. Continuity properties. Markov and strong Markov property and applications. Donsker’s invariance principle. Further sample path properties.  

Suggested books and references:

1. Rick Durrett, Probability: theory and examples., Cambridge University Press, 2010..
2. David Williams, Probability with Martingales, Cambridge Univ., Press, 1991.
3. Peter Mörters and Yuval Peres, Brownian motion, Cambridge University Press, 2010..
4. Olav Kallenberg, Foundations of modern Probability. Second Edition, Springer-Verlag, 2002..
5. John Walsh, Knowing the Odds: An Introduction to Probability, AMS, 2012..

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