Realization of Levy flights as continuous processes

Details Realization of Levy flights as continuous processes Realization of Levy flights as continuous processes

2007-06-28

arxiv.org/abs/0706.4320v1

Physics

Condensed Matter

Statistical Mechanics

paper of 5 pages with 3 figures with added supplementary materials

Scientific paper

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.

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