Directed transport induced by spatially modulated Lévy flights

In this paper we study the dynamics of a particle in a ratchet potential subject to multiplicative -stable Lévy noise, α ∈ (0,2], in the limit of a noise amplitude ε → 0. We compare the dynamics for Itô and Marcus multiplicative noises and obtain the explicit asymptotics of the escape time in the wells and transition probabilities between the wells. A detailed analysis of the noise-induced current is performed for the Seebeck ratchet with a weak multiplicative noise for α ∈ (0,2].