Realization of Levy flights as continuous processes
Statistical Mechanics
2007-07-02 v1 Materials Science
Abstract
On the basis of multivariate Langevin processes we present a realization of Levy flights as a continuous process. For the simple case of a particle moving under the influence of friction and a velocity dependent stochastic force we explicitly derive the generalized Langevin equation and the corresponding generalized Fokker-Planck equation describing Levy flights. Our procedure is similar to the treatment of the Kramers-Fokker Planck equation in the Smoluchowski limit. The proposed approach forms a feasible way of tackling Levy flights in inhomogeneous media or systems with boundaries what is up to now a challenging problem.
Keywords
Cite
@article{arxiv.0706.4320,
title = {Realization of Levy flights as continuous processes},
author = {Ihor Lubashevsky and Rudolf Friedrich and Andreas Heuer},
journal= {arXiv preprint arXiv:0706.4320},
year = {2007}
}