Lévy anomalous diffusion and fractional Fokker–Planck equation

V.V. Yanovsky, A.V. Chechkin, D. Schertzer and A.V. Tur

Physica A: Statistical Mechanics and its Applications, 2000, vol. 282, issue 1, 13-34

Abstract: We demonstrate that the Fokker–Planck equation can be generalized into a ‘fractional Fokker–Planck’ equation, i.e., an equation which includes fractional space differentiations, in order to encompass the wide class of anomalous diffusions due to a Lévy stable stochastic forcing. A precise determination of this equation is obtained by substituting a Lévy stable source to the classical Gaussian one in the Langevin equation. This yields not only the anomalous diffusion coefficient, but a non-trivial fractional operator which corresponds to the possible asymmetry of the Lévy stable source. Both of them cannot be obtained by scaling arguments. The (mono-) scaling behaviors of the fractional Fokker–Planck equation and of its solutions are analysed and a generalization of the Einstein relation for the anomalous diffusion coefficient is obtained. This generalization yields a straightforward physical interpretation of the parameters of Lévy stable distributions. Furthermore, with the help of important examples, we show the applicability of the fractional Fokker–Planck equation in physics.

Keywords: Diffusion; Transport; Statistical physics; Stochastic systems; Scaling; Renormalization (search for similar items in EconPapers)
Date: 2000
References: View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437199005658
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:282:y:2000:i:1:p:13-34

DOI: 10.1016/S0378-4371(99)00565-8

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().