Stability with respect to a part of the variables of stochastic di erential equations driven by G-Brownian motion

Abstract

In this paper, we investigate the pth moment exponential stability of stochastic dif- ferential equations driven by G-Brownian motion (G-SDEs) with respect to a part of the variables by means of the G-Lyapunov functions and recently developed It^o's calculus for SDEs driven by G-Brownian motion, as well as Gronwall's inequalities. We establish suf- cient conditions to ensure the quasi sure exponential stability of stochastic di erential equations perturbed by G-Brownian motion with respect to a part of the variables. Some illustrative examples to show the usefulness of the stability with respect to a part of the variables notion are also provided.