Exponential stability of SDEs driven by $G$-Brownian motion with delayed impulsive effects: average impulsive interval approach

Yong Ren; Wensheng Yin; Dongjin Zhu

doi:10.3934/dcdsb.2018248

Article Contents

2018, Volume 23, Issue 8: 3347-3360. Doi: 10.3934/dcdsb.2018248

This issue Previous Article Poisson $S^2$-almost automorphy for stochastic processes and its applications to SPDEs driven by Lévy noise Next Article On geometric conditions for reduction of the Moreau sweeping process to the Prandtl-Ishlinskii operator

Exponential stability of SDEs driven by $G$-Brownian motion with delayed impulsive effects: average impulsive interval approach

Department of Mathematics, Anhui Normal University, Wuhu 241000, China

* Corresponding author: Yong Ren
* Corresponding author: Yong Ren

Received: January 2018

Early access: August 20, 2018

Published online: August 20, 2018

The first author is supported by the National Natural Science Foundation of China grant 11371029 and 11501009

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Abstract

In this article, we discuss a class of impulsive stochastic function differential equations driven by $G $-Brownian motion with delayed impulsive effects ($G $-DISFDEs, in short). Some sufficient conditions for $p$-th moment exponential stability of $G $-DISFDEs are derived by means of $G $-Lyapunov function method, average impulsive interval approach and Razumikhin-type conditions. An example is provided to show the effectiveness of the theoretical results.

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Mathematics Subject Classification: Primary: 93E15, 34K50, 60H10.

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