Exponential stability for stochastic differential equation driven by G-Brownian motion

Consider a stochastic differential equation driven by G-Brownian motion dX(t) = AX (t)dt + sigma (t, X (t))dB(t) which might be regarded as a stochastic perturbed system of dX(t) = AX(t)dt. Suppose the second equation is quasi surely exponentially stable. In this paper. we investigate the sufficient conditions under which the first equation is still quasi surely exponentially stable. (C) 2012 Elsevier Ltd. All rights reserved.