Densities for Ornstein–Uhlenbeck processes with jumps

We consider an Ornstein–Uhlenbeck process with values in R_n driven by a Levy process (Z_t)
taking values in R_d with d possibly smaller than n. The Levy noise can have a degenerate or even
vanishing Gaussian component. Under a controllability rank condition and a mild assumption
on the Levy measure of (Z_t), we prove that the law of the Ornstein–Uhlenbeck process at any
time t > 0 has a density on R_n.