Existence of a limit distribution of a solution of a linear inhomogeneous stochastic differential equation

We find conditions for the existence of a limit distribution (as $t\rightarrow\infty$) of a vector process $\xi$ defined in $\mathbb{R}_+$ and determined by an inhomogeneous stochastic differential equation $\xi(t)=\xi(0)-\xi\circ\alpha+f\ast\nu+g\ast\mu$, where $\alpha$ is a nonrandom continuous increasing function, $\nu$ and $\mu$ are independent Poisson and centered Poisson measures, respectively.