Rounding Error in Numerical Solution of Stochastic Differential Equations

Dr. Armando Arciniega

Department of Mathematics
Texas Tech University

March 4, 2003
200 Madison Hall
11:00 PM (Coffee and Cookies at 10:30)

Abstract

The study of stochastic differential equations plays a prominent role in a range of application areas. When a differential equation model for some physical phenomenon is formulated, one would like to obtain the exact solution. However, even for ordinary differential equations this is generally not possible and numerical methods must be used. The present investigation is concerned with estimating the rounding error in numerical solution of stochastic differential equations. A statistical rounding error anlaysis in Euler's method for numerical solution of stochastic differential equations is performed. It is shown that the rounding error is inversely proportional to the square root of the step size. An extrapolating technique is applied to functional expectation of the numerical solutions. Richardson extrapolation provides second-order accuracy, and is one way to increase accuracy while avoiding rounding error.