Multiplicative Levy noise in bistable systems

Abstract

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

8 pages, 6 figures

References in corpus (8)

• The scaling laws of human travel
• Fractional Fokker--Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises
• Anomalous jumping in a double-well potential
• Escape driven by $\alpha$-stable white noises
• Levy Flights in Inhomogeneous Media
• Levy stable noise induced transitions: stochastic resonance, resonant activation and dynamic hysteresis
• Multiplicative Lévy processes: Itô versus Stratonovich interpretation
• Nonlinear stochastic equations with multiplicative Lévy noise

Cited by in corpus (3)

• Lévy on-off intermittency
• Random acceleration process on finite intervals under stochastic restarting
• Bistable generalised Langevin dynamics driven by correlated noise possessing a long jump distribution: barrier crossing and stochastic resonance