Mean Square Stability of a Class of Runge-Kutta Methods for 2-Dimensional Stochastic Differential Systems

Abstract

Despite the intensive work done on developing numerical schemes for stochastic differential equations, stability analysis of these schemes when applied to stochastic differential systems is still under premature stage. Motivated by the work of Saito and Mitsui in [11], we investigate mean square stability for a class of weak second order Runge-Kutta schemes applied to 2-dimensional stochastic differential systems. Stability criteria will be established, and numerical examples in support of the theoretical analysis will be provided. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)