Mixtures in non stable Levy processes

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dc.creatorPetroni, Nicola Cufaro
dc.date2007-02-02
dc.date.accessioned2026-07-07T12:16:58Z
dc.date.available2026-07-07T12:16:58Z
dc.descriptionWe analyze the Levy processes produced by means of two interconnected classes of non stable, infinitely divisible distribution: the Variance Gamma and the Student laws. While the Variance Gamma family is closed under convolution, the Student one is not: this makes its time evolution more complicated. We prove that -- at least for one particular type of Student processes suggested by recent empirical results, and for integral times -- the distribution of the process is a mixture of other types of Student distributions, randomized by means of a new probability distribution. The mixture is such that along the time the asymptotic behavior of the probability density functions always coincide with that of the generating Student law. We put forward the conjecture that this can be a general feature of the Student processes. We finally analyze the Ornstein--Uhlenbeck process driven by our Levy noises and show a few simulation of it.
dc.description28 pages, 3 figures, to be published in J. Phys. A: Math. Gen
dc.identifierhttps://arxiv.org/abs/math/0702058
dc.identifierhttp://arxiv.org/abs/math/0702058
dc.identifierJ.Phys.A40:2227-2250,2007
dc.identifierdoi:10.1088/1751-8113/40/10/001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/211975
dc.subjectProbability
dc.subjectStatistical Mechanics
dc.subjectAccelerator Physics
dc.subjectComputational Finance
dc.subject60E07, 60G10, 60G51, 60J75
dc.titleMixtures in non stable Levy processes
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