Stability of neutral stochastic functional differential equations with Markovian switching driven by G-Brownian motion

Abstract

Little seems to be known about stability results on the neutral stochastic function differential equations with Markovian switching driven by G-Brownian (G-NSFDEwMSs). This paper aims at investigating the pth moment exponential stability for G-NSFDEwMSs to fill this gap. Some sufficient conditions on the pth moment exponential stability of the trivial solution are derived by employing the Razumikhin-type method, stochastic analysis, and algebraic inequality technique. Moreover, an example is provided to illustrate the effectiveness of the obtained results.

Keywords:

• pth Moment exponential stability
• neutral stochastic functional differential equations
• G-Brownian motion
• Markovian switching
• Razumikhin-type theorems

AMS Subject Classifications:

• 93E15
• 60H10
• 34K50

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 [grant number 11671149]; the Natural Science Foundation of Guangdong Province [grant number 2014A030313256].