Geodesic
Ultrafast Subordinators and Their Hitting Times
Publications de l'Institut Mathématique, _N_S_80 (2006) no. 94, p. 193 .

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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.
DOI : 10.2298/PIM0694193K
Classification : 60G50 60F17 60H30 82C31
Mots-clés : regular variation, anomalous diffusion, subordinator, hitting time 
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Mihály Kovács; Mark M. Meerschaert. Ultrafast Subordinators and Their Hitting Times. Publications de l'Institut Mathématique, _N_S_80 (2006) no. 94, p. 193 . doi : 10.2298/PIM0694193K. https://geodesic-test.mathdoc.fr/articles/10.2298/PIM0694193K/

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