Eventual uniform asymptotic stability for stochastic differential equation based on semimartingale with spatial parameter

Given a stochastic differential equation based on semimartingale with spatial parameter (1) $$\varphi _t = x_0 + \int_{t_0 }^t {F(\varphi _s ,ds) } on t \geqslant t_0 $$ and it perturbed system (2) $$\psi _t = x_0 + \int_{t_0 }^t {F\left( {\psi \alpha _s , ds} \right)} + \int_{t_0 }^t {G\left( {\psi _s , ds} \right)} on t \geqslant t_0 $$ In this paper we give some sufficient conditions under which the eventual uniform asymptotic stability of Eq. (1) is shared by Eq. (2).