Realization of Lévy walks as Markovian stochastic processes.
Based on multivariate Langevin processes we present a realization of Lévy 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 Lévy flights. Our procedure is similar to the treatment of the Kramers-Fokker-Planck equation in the Smoluchowski limit. The proposed approach may open a way to treat Lévy flights in inhomogeneous media or systems with boundaries in the future.
Lubashevsky
Ihor
I
A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Vavilov Strasse 38, 119991 Moscow, Russia.
Friedrich
Rudolf
R
Heuer
Andreas
A