The p-th moment stability of solutions to impulsive stochastic differential equations driven by G-Brownian motion

Abstract

In this paper, we consider a class of impulsive stochastic differential equations driven by G-Brownian motion (IGSDEs in short). By means of the G-Lyapunov function method, some criteria on p-th moment stability and p-th moment asymptotical stability for the trivial solutions of IGSDEs are established. An example is presented to illustrate the efficiency of the obtained results.

Keywords:

• Stochastic differential equation
• G-Brownian motion
• p-th moment stability
• p-th moment asymptotical stability
• Lyapunov function method

AMS Subject Classifications:

• 93E15
• 60H10

Acknowledgements

The authors wish to thank the two anonymous referees for their valuable comments, correcting errors and improving written language.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11371029]; Natural Science Foundation of Anhui Province [grant number 1508085JGD10].