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

Consider a stochastic differential equation driven by G-Brownian motion d X ( t ) = A X ( t ) d t + σ ( t , X ( t ) ) d B t which might be regarded as a stochastic perturbed system of d X ( t ) = A X ( t ) d t . 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.