Department of Mathematics

INDIAN INSTITUTE OF SCIENCE

MA 362: Stochastic Processes

Credits: 3:0

Prerequisite courses: MA361

First Construction of Brownian Motion, convergence in $C[0,\infty)$, $D[0,\infty)$, Donsker’s invariance principle, Properties of the Brownian motion, continuous-time martingales, optional sampling theorem, Doob-Meyer decomposition, stochastic integration, Ito’s formula, martingale representation theorem, Girsanov’s theorem, Brownian motion and the heat equation, Feynman- Kac formula, diffusion processes and stochastic differential equations, strong and weak solutions, martingale problem.

Suggested books and references:

1. P. Billingsley, Convergence of probability measures
2. Karatzas and Shreve, Brownian motion and stochastic calculus
3. Revuz and Yor, Continuous martingales and Brownian motion
4. A. Oksendal, Introduction to stochastic differential equations

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