  Stochastic motion in a bistable, periodically modulated potential is
discussed. The system is stimulated by a white noise increments of which have a
symmetric stable L\'evy distribution. The noise is multiplicative: its
intensity depends on the process variable like |x|^{-\theta}. The Stratonovich
and It\^o interpretations of the stochastic integral are taken into account.
The mean first passage time is calculated as a function of \theta for different
values of the stability index \alpha and size of the barrier. Dependence of the
output amplitude on the noise intensity reveals a pattern typical for the
stochastic resonance. Properties of the resonance as a function of \alpha,
\theta\ and size of the barrier are discussed. Both height and position of the
peak strongly depends on \theta\ and on a specific interpretation of the
stochastic integral.
