Multiplicative Levy noise in bistable systems

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 Levy distribution. The noise is multiplicative: its intensity depends on the process variable like vertical bar x vertical bar(-theta). The Stratonovich and Ito 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 a 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.