Stationary states in Langevin dynamics under asymmetric Lévy noises

Abstract

Properties of systems driven by white non-Gaussian noises can be very different from these of systems driven by the white Gaussian noise. We investigate stationary probability densities for systems driven by alpha-stable Lévy-type noises, which provide natural extension to the Gaussian noise having, however, a new property, namely a possibility of being asymmetric. Stationary probability densities are examined for a particle moving in parabolic, quartic, and in generic double well potential models subjected to the action of alpha-stable noises. Relevant solutions are constructed by methods of stochastic dynamics. In situations where analytical results are known they are compared with numerical results. Furthermore, the problem of estimation of the parameters of stationary densities is investigated.