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Anomalous diffusion and the first passage time problem

Rangarajan, Govindan and Ding, Mingzhou (2000) Anomalous diffusion and the first passage time problem. In: Physical Review E, 62 (1). pp. 120-133.

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We study the distribution of the first passage time (FPT) in Levy type anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in terms of Fox or H functions when the diffusion has zero drift.(2) For the nonzero drift case we obtain an analytical expression for the Laplace transform of the FPT distribution.(3) We express the FPT distribution in terms of a power series for the case of two absorbing barriers. The known results for ordinary diffusion (Brownian motion) are obtained as special cases of our more general results.

Item Type: Journal Article
Publication: Physical Review E
Publisher: American Institute of Physics
Additional Information: Copyright of this article belongs to American Institute of Physics.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 18 Aug 2006
Last Modified: 19 Sep 2010 04:30
URI: http://eprints.iisc.ac.in/id/eprint/8076

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