Anomalous diffusion and generalized Sparre Andersen scalingB. Dybiec and E. Gudowska-Nowak
Marian Smoluchowski Institute of Physics, and Mark Kac Center for Complex Systems Research Jagellonian University - ul. Reymonta 4, 30-059 Kraków, Poland, EU
received 8 June 2009; accepted in final form 16 September 2009; published October 2009
published online 16 October 2009
We are discussing the long-time scaling limit for the anomalous diffusion composed of the subordinated Lévy-Wiener process. The limiting anomalous diffusion is in general non-Markov, even in the regime, where ensemble averages of a mean-square displacement or quantiles representing the group spread of the distribution follow the scaling characteristic for an ordinary stochastic diffusion. To discriminate between a truly memory-less process and the non-Markov one, we are analyzing the deviation of the survival probability from the (standard) Sparre Andersen scaling.
05.40.Fb - Random walks and Levy flights.
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.).
02.50.-r - Probability theory, stochastic processes, and statistics.
© EPLA 2009