Stationary states in Langevin dynamics under asymmetric Lévy noises

Details Stationary states in Langevin dynamics under asymmetric Lévy noises Stationary states in Langevin dynamics under asymmetric Lévy noises

2007-02-07

arxiv.org/abs/cond-mat/0702182v2

Phys. Rev. E. 76, 041122 (2007)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 9 figures, 3 tables

Scientific paper

10.1103/PhysRevE.76.041122

Properties of systems driven by white non-Gaussian noises can be very different from these systems driven by the white Gaussian noise. We investigate stationary probability densities for systems driven by $\alpha$-stable L\'evy type noises, which provide natural extension to the Gaussian noise having however a new property mainly 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.

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