Realization of Levy walks as Markovian stochastic processes

被引：25

作者：

Lubashevsky, Ihor ^{[1
,2
,3
]}

Friedrich, Rudolf ^{[4
,5
]}

Heuer, Andreas ^{[2
,5
]}

机构：

[1] Russian Acad Sci, AM Prokhorov Gen Phys Inst, Moscow 119991, Russia

[2] Univ Munster, Inst Phys Chem, D-48149 Munster, Germany

[3] Moscow Tech Univ Radioengn, Moscow 119454, Russia

[4] Univ Munster, Inst Theoret Phys, D-48149 Munster, Germany

[5] Univ Munster, Ctr Nonlinear Sci CeNoS, D-48149 Munster, Germany

来源：

PHYSICAL REVIEW E | 2009年 / 79卷 / 01期

关键词：

Brownian motion; Fokker-Planck equation; Markov processes; transport processes; EXTERNAL FORCE-FIELDS; ANOMALOUS DIFFUSION; FLIGHTS; EQUATIONS; LANGEVIN; MODELS; TIME;

D O I：

10.1103/PhysRevE.79.011110

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

Based on 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 may open a way to treat Levy flights in inhomogeneous media or systems with boundaries in the future.

引用

页数：5

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