Mean-square stability of the Euler–Maruyama method for stochastic differential delay equations with jumps

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.

Keywords:

• stochastic differential delay equations
• Poisson jumps
• Euler–Maruyama method
• MS-stability

2000 AMS Subject Classifications :

• 60H10
• 60B05
• 62L20
• 93E15
• 65C30

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.

Additional information

Notes on contributors

Jianguo Tan

Current address: Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China.