  Properties of systems driven by white non-Gaussian noises can be very
different from these systems driven by the white Gaussian noise. We investigate
stationary probability densities for systems driven by $\alpha$-stable L\'evy
type noises, which provide natural extension to the Gaussian noise having
however a new property mainly a possibility of being asymmetric. Stationary
probability densities are examined for a particle moving in parabolic, quartic
and in generic double well potential models subjected to the action of
$\alpha$-stable noises. Relevant solutions are constructed by methods of
stochastic dynamics. In situations where analytical results are known they are
compared with numerical results. Furthermore, the problem of estimation of the
parameters of stationary densities is investigated.
