Convergence and stability of impulsive stochastic differential equations

ABSTRACT

In this paper, we consider impulsive stochastic differential equations. We show that these equations are the exponentially stable in the mean-square sense under Lipschitz conditions. We also construct the numerical method and prove the method is strongly convergent and exponentially stable in the mean-square sense. Moreover, we give some examples in order to illustrate the main results.

KEYWORDS:

• Impulsive stochastic differential equations
• transformed-Euler method
• convergence
• exponential stability
• simulation

2010 AMS SUBJECT CLASSIFICATIONS:

• 60H10
• 60H35
• 93E15
• 65C20

Acknowledgments

The authors thank the referees and the editors for their valuable detailed comments and helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by NSF of China [No. 11671113].