Stability of stochastic θ-methods for stochastic delay integro-differential equations

Abstract

In this paper, we are concerned with the numerical stability of linear stochastic delay integro-differential equations (SDIDEs). A sufficient condition for mean square stability of the exact solution of a linear SDIDE with multiplicative noise is derived. Then the mean square stability of stochastic θ-methods is investigated, and it is shown that the numerical solution can reproduce the mean square stability of the exact solution under appropriate conditions. At last, we present some numerical experiments to support our conclusions.

Keywords:

• linear stochastic delay integro-differential equations
• numerical solution
• stochastic θ-methods
• mean square stability

2000 AMS Subject Classifications :

• 65C30
• 60H35
• 65L20

Acknowledgements

The authors are indebted to the referees and the editors for their careful reading of this paper and for their valuable comments. This work is supported by NSF of China (No. 10971077).