### MA 362: Stochastic Processes

#### 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 .

#### All Courses

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265
E-mail: chairman.math[at]iisc[dot]ac[dot]in