Boundedness and stability analysis for impulsive stochastic differential equations driven by G-Brownian motion

ABSTRACT

In this article, the pth moment globally exponential ultimate boundedness, pth moment globally exponential stability, quasi sure globally exponential boundedness and quasi sure globally exponential stability are investigated for impulsive stochastic differential equations driven by G-Brownian motion. Using G-Lyapunov function methods and inequality techniques, some sufficient conditions are derived for the boundedness and stability. Comparing with the existing methods, the obtained results allow the corresponding impulse-free systems to be unstable and unbounded. An example is provided to show the effectiveness of the theoretical results.

KEYWORDS:

• Impulsive stochastic differential systems
• G-Brownian motion
• exponential ultimate boundedness
• quasi sure exponential boundedness

Acknowledgments

The authors would like to thank the anonymous reviewers for their insightful comments that have helped improve the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work is supported by the National Natural Science Foundation of China [grant number 11501518], [grant number 11401382].