Stability of square-mean almost automorphic mild 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). In particular, we study the exponentially and quasi sure exponential stability of the square-mean almost automorphic solutions of the IGSDEs. Specifically by employing the Lyapunov function method, a new set of sufficient conditions is derived for obtaining the required result.

Keywords:

• Square-mean almost automorphic
• stochastic differential equations
• G-Brownian motion
• exponentially stability in mean square
• Lyapunov function method

Acknowledgments

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

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (11871076).