  Dynamical systems driven by a general L\'evy stable noise are considered. The
inertia is included and the noise, represented by a generalised
Ornstein-Uhlenbeck process, has a finite relaxation time. A general linear
problem (the additive noise) is solved: the resulting distribution converges
with time to the distribution for the white-noise, massless case. Moreover, a
multiplicative noise is discussed. It can make the distribution steeper and the
variance, which is finite, depends sublinearly on time (subdiffusion). For a
small mass, a white-noise limit corresponds to the Stratonovich interpretation.
On the other hand, the distribution tails agree with the Ito interpretation if
the inertia is very large. An escape time from the potential well is
calculated.
