Prabhakar Lévy processes

Janusz Gajda and Luisa Beghin

Statistics & Probability Letters, 2021, vol. 178, issue C

Abstract: We introduce here a generalization of the Mittag-Leffler Lévy process (with parameter α), obtained by extending its Lévy measure through the Prabhakar function (which is a Mittag-Leffler with the additional parameters β and γ). We prove that this so-called Prabhakar process, in the special case β=1, can be represented as an α-stable process subordinated by an independent generalized gamma subordinator; thus it can be considered as an extension of the geometric stable process, to which it reduces for γ=1. On the other hand, for α=β=1, it coincides with the generalized gamma process itself. Therefore, by suitably specifying the three parameters, the Prabhakar process turns out to represent an interpolation among various well-known and widely applied stochastic models.

Keywords: Mittag-Leffler distribution; Subordinated; Stochastic processes; Lévy density (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2021.109162

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