Venue: TBA
Class Timings: 9:30 AM
First Meeting: 4 September 2026
Course Description: TBA
Syllabus:
- Discrete time Markov chains: for countable state space, classification of states.
- Discrete parameter martingales: conditional expectation, optional sampling theorems, Doob’s inequalities, martingale convergence theorems.
- Brownian motion: construction, continuity properties. Markov and strong Markov property and applications, Donsker’s invariance principle, sample path properties.
Prerequisites: A first course in probability, together with basic familiarity with real analysis and measure theory, is recommended.
References:
- Reversible Markov Chains and Random Walks on Graphs by David Aldous and Jim Fill.
- Discrete Stochastic Processes by Robert Gallagher
- I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Graduate Texts in Mathematics, Springer.
Course Outcomes: The students will have an understanding of the Markov Chains, Martingales and fundamental properties of Brownian motion and the probabilistic framework underlying stochastic calculus.
Course Evaluation: TBA
- Teacher: Siva Athreya
Credit Score: 4