  A harmonic oscillator under influence of the noise is a basic model of
various physical phenomena. Under Gaussian white noise the position and
velocity of the oscillator are independent random variables which are
distributed according to the bivariate Gaussian distribution with elliptic
level lines. The distribution of phase is homogeneous. None of these properties
hold in the general L\'evy case. Thus, the level lines of the joint probability
density are not elliptic. The coordinate and the velocity of the oscillator are
strongly dependent, and this dependence is quantified by introducing the
corresponding parameter ("width deficit"). The distribution of the phase is
inhomogeneous and highly nontrivial.
