Department of Mathematics

INDIAN INSTITUTE OF SCIENCE

MA 362: Stochastic Processes

Credits: 3:0

Prerequisite courses: MA361

Construction and sample path properties of Brownian motion. Strong Markov property. Martingales in Brownian motion. Long term behaviour. Skorokhod embedding and Donsker’s theorem.

Continuous time martingales, quadratic variation. Stochastic integration with respect to continuous semi-martingales. Ito’s formula. Introduction to diffusions.

Suggested books and references:

1. Richard Bass, Stochastic processes, Cambridge university press (2012)..
2. J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016).
3. Morters and Peres, Brownian motion, Cambridge university press (2012).
4. Oksendal, Stochastic differential equations, Springer (2014).
5. S. R. S. Varadhan, Lectures on Diffusion Problems and Partial Differential Equations, TIFR lecture series (1980).
6. R. L. Karandikar and B. V. Rao, Introduction to Stochastic Calculus, Springer (2018).

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