Parameters of the fractional Fokker-Planck equationS. I. Denisov1, 2, P. Hänggi3 and H. Kantz1
1 Max-Planck-Institut für Physik Komplexer Systeme - Nöthnitzer Straße 38, D-01187 Dresden, Germany
2 Department of Physics, Sumy State University - 2 Rimsky-Korsakov Street, 40007 Sumy, Ukraine
3 Institut für Physik, Universität Augsburg - Universitätsstraße 1, D-86135 Augsburg, Germany
received 7 November 2008; accepted in final form 30 January 2009; published February 2009
published online 6 March 2009
We study the connection between the parameters of the fractional Fokker-Planck equation, which is associated with the overdamped Langevin equation driven by noise with heavy-tailed increments, and the transition probability density of the noise generating process. Explicit expressions for these parameters are derived both for finite and infinite variance of the rescaled transition probability density.
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.).
05.40.Fb - Random walks and Levy flights.
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