Realization of Levy flights as continuous processes

Ihor Lubashevsky; Rudolf Friedrich; Andreas Heuer

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arXiv · 0706.4320

Realization of Levy flights as continuous processes

Ihor Lubashevsky·Rudolf Friedrich·Andreas Heuer

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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.

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Ihor Lubashevsky, Rudolf Friedrich, Andreas Heuer. 2007-06-28. Realization of Levy flights as continuous processes. https://arxiv.org/abs/0706.4320

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