| Abstract: | Consider a nonlinear stochastic differential equations with respect to semimartingales (1) dY(t) = F{Y(t),t)dti(t) + G(t)dM(t)+f(Y(t),t)dti(t)+g(Y(t),t)dM(t), which might be regarded as a stochastic perturbed system of (2) dX(t) = F(X(t),t)dfi(t) + G(t)dM(t). Suppose Eq. (2) is exponentially stable almost surely. Under what conditions is Eq. (1) still exponentially stable almost surely? In this paper we will give some sufficient conditions. As an application we also discuss the almost sure exponential stability for semilinear stochastic systems and small stochastic perturbed systems |
