DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Harbir Lamba, Mathematics, George Mason University

**Title: ***
The Efficient Numerical Solution of Stochastic Differential Equations
*

**Abstract:**
Mathematical models incorporating random forcing, and the resulting stochastic differential equations, are becoming increasingly important. However general principles and techniques for their robust and efficient numerical approximation are a very long way behind the corresponding ODE theory. In both cases the idea of adaptivity, that is using varying timesteps to improve convergence, is a key element.
In this talk I will describe a general approach based upon (low-order) Milstein-type methods using multiple error-controls. The idea is to monitor various terms in the truncation error, both deterministic and stochastic, and then to construct an algorithm that is robust enough to work efficiently in the presence of both drift- and diffusion-dominated regimes and differing accuracy requirements. The form of the error controls suggests a novel timestepping procedure that chooses the timestep to be the first-exit-time of the Brownian motion from a simple domain. The approach also has other benefits, such as improved numerical stability properties. No knowledge of stochastic calculus will be assumed.

**Place:** Science and Technology Building I, Room 242

** Presentation files: ** [pdf]

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491