Abstract
This paper deals with the mean-square (MS) stability of the Euler–Maruyama method for stochastic differential delay equations (SDDEs) with jumps. First, the definition of the MS-stability of numerical methods for SDDEs with jumps is established, and then the sufficient condition of the MS-stability of the Euler–Maruyama method for SDDEs with jumps is derived, finally a class scalar test equation is simulated and the numerical experiments verify the results obtained from theory.
Acknowledgements
This research was supported with funds provided by the National Natural Science Foundation of China (No. 10732020). We thank two anonymous reviewers for their very valuable comments and helpful suggestions which improved this paper significantly.