First Passage Time Distribution for Anomalous Diffusion

Details First Passage Time Distribution for Anomalous Diffusion First Passage Time Distribution for Anomalous Diffusion

2001-05-14

arxiv.org/abs/cond-mat/0105266v1

Phys. Lett. A273 (2000) 322-330

Physics

Condensed Matter

Statistical Mechanics

11 pages, 2 figures

Scientific paper

10.1016/S0375-9601(00)00518-1

We study the first passage time (FPT) problem in Levy type of anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation, we obtain an analytic expression for the FPT distribution which, in the large passage time limit, is characterized by a universal power law. Contrasting this power law with the asymptotic FPT distribution from another type of anomalous diffusion exemplified by the fractional Brownian motion, we show that the two types of anomalous diffusions give rise to two distinct scaling behavior.

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