Exponential stability of solutions to impulsive stochastic differential equations driven by  $G$-Brownian motion

Yong  Ren; Xuejuan  Jia; Lanying  Hu

doi:10.3934/dcdsb.2015.20.2157

Article Contents

2015, Volume 20, Issue 7: 2157-2169. Doi: 10.3934/dcdsb.2015.20.2157

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Exponential stability of solutions to impulsive stochastic differential equations driven by $G$-Brownian motion

1.
Department of Mathematics, Anhui Normal University, Wuhu 241000, Anhui
2.
Department of Mathematics, Anhui Normal University, Wuhu 241000, Anhui,

Received: July 31, 2014

Revised: February 28, 2015

Published: August 2015

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Abstract

In this paper, we establish the $p$-th moment exponential stability and quasi sure exponential stability of the solutions to impulsive stochastic differential equations driven by $G$-Brownian motion (IGSDEs in short) by means of $G$-Lyapunov function method. An example is presented to illustrate the efficiency of the obtained results.

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Mathematics Subject Classification: Primary: 34A37, 60H10; Secondary: 34D10.

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