From Power Laws to Fractional Diffusion: the Direct Way

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dc.creatorGorenflo, Rudolf
dc.creatorAbdel-Rehim, Entsar A. A.
dc.date2007-12-30
dc.date.accessioned2026-07-07T08:51:57Z
dc.date.available2026-07-07T08:51:57Z
dc.descriptionStarting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for the waiting times, between 0 and 2 for the jumps. By stating the relevant lemmata (of Tauber type) for the distribution functions we need not distinguish between continuous and discrete space and time. We will see that, by a well-scaled passage to the diffusion limit, generalized diffusion processes, fractional in time as well as in space, are obtained. The corresponding equation of evolution is a linear partial pseudo-differential equation with fractional derivatives in time and in space, the orders being equal to the above exponents. Such processes are well approximated and visualized by simulation via various types of random walks. For their explicit solutions there are available integral representations that allow to investigate their detailed structure.
dc.description12 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/0801.0142
dc.identifierhttp://arxiv.org/abs/0801.0142
dc.identifierVietnam Journal of Mathematics, Vol. 32 (SI), 65-75 (2004)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145115
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject26A33, 33E12, 45E10, 45K05, 60F05, 60G50, 60J60
dc.titleFrom Power Laws to Fractional Diffusion: the Direct Way
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