Stationary states in Langevin dynamics under asymmetric Lévy noises

B. Dybiec, E. Gudowska-Nowak, and I. M. Sokolov
Phys. Rev. E 76, 041122 – Published 16 October 2007

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 α-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 α-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.

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  • Received 7 February 2007

DOI:https://doi.org/10.1103/PhysRevE.76.041122

©2007 American Physical Society

Authors & Affiliations

B. Dybiec* and E. Gudowska-Nowak

  • M. Smoluchowski Institute of Physics and Mark Kac Center for Complex Systems Research, Jagellonian University, ul. Reymonta 4, 30–059 Kraków, Poland

I. M. Sokolov

  • Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, D–12489 Berlin, Germany

  • *bartek@th.if.uj.edu.pl
  • gudowska@th.if.uj.edu.pl
  • igor.sokolov@physik.hu-berlin.de

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Issue

Vol. 76, Iss. 4 — October 2007

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