Numerical Solution to Hybrid Stochastic Differential Systems

Abstract

In this article numerical methods for solving hybrid stochastic differential systems of Itô-type are developed by piecewise application of numerical methods for SDEs. We prove a convergence result if the corresponding method for SDEs is numerically stable with uniform convergence in the mean square sense. The Euler and Runge–Kutta methods for hybrid stochastic differential equations are specifically described and the order of the error is given for the Euler method. A numerical example is given to illustrate the theory.

Keywords:

• Hybrid systems
• Itô-type equations
• Numerical stability
• Stochastic differential equations
• Uniform convergence

Mathematics Subject Classification:

• 65C30
• 34F05
• 60H10