EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 80(94), pp. 193–206 (2006)

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ULTRAFAST SUBORDINATORS AND THEIR HITTING TIMES

Mihaly Kovacs and Mark M. Meerschaert

Department of Mathematics & Statistics, University of Otago, New Zealand and Department of Statistics & Probability, Michigan State University, A416 Wells Hall, East Lansing, MI 48824-1027 USA

Abstract: Ultrafast subordinators are nondecreasing Lévy processes obtained as the limit of suitably normalized sums of independent random variables with slowly varying probability tails. They occur in a physical model of ultraslow diffusion, where the inverse or hitting time process randomizes the time variable. In this paper, we use regular variation arguments to prove that a wide class of ultrafast subordinators generate holomorphic semigroups. We then use this fact to compute the density of the hitting times. The density formula is important in the physics application, since it is used to calculate the solutions of certain distributed-order fractional diffusion equations.

Keywords: regular variation, anomalous diffusion, subordinator, hitting time

Classification (MSC2000): 60G50; 60F17; 60H30; 82C31

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Electronic fulltext finalized on: 10 Oct 2006. This page was last modified: 4 Dec 2006.

© 2006 Mathematical Institute of the Serbian Academy of Science and Arts
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