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.