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��vy distribution. The noise is multiplicative: its intensity depends on the process variable like |x|^{-��}. The Stratonovich and It�� interpretations of the stochastic integral are taken into account. The mean first passage time is calculated as a function of ��for different values of the stability index ��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 ��, �� and size of the barrier are discussed. Both height and position of the peak strongly depends on �� and on a specific interpretation of the stochastic integral.

8 pages, 6 figures