### MA 5312 Stochastic Differential Equations

#### Course Details

Introduction: Stochastic analogs of classical differential equations.

Mathematica; preliminaries: Probability space, random variable, stochastic process, Brownian motion.

Ito Integral: Definition, Properties, extensions.

Ito formula and Martingale representation Theorem: One-dimensional Ito formula, Multi-dimensional Ito formula, Martingle representation Theorem.

Stochastic differential equations: Examples and some solution methods, Existence an Uniqueness result, weak and strong solutions.

Applications: Boundary valur problems, filtering, optimal stopping, stochastic control, mathematical finance.

#### Course References:

Text Books:

1. B. K. Oksendal, Stochastic Differential Equations: An Introduction with Applications, 6th edition, Apringer, 2010.

Reference:

1. I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calxulus, SPringer, 1991.

2. P. Protter, Stochastic Integration and Diferential Equations, Springer, 2nd edition. 2010.

3. I. Karatzas and S.E. Shreve, Methods of Mathematical Finance, Springer, 2010.

4. S. Watanabe and N. Ikeda, Stochastic Differential Equations and Diffusion Processes, North-Holland, 1981.