English

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}
}
R2 v1 2026-06-21T08:50:28.384Z