The space-fractional Poisson process is a time-changed homogeneous Poisson process where the time change is an independent stable subordinator. In this paper, a further generalization is discussed that preserves the Lévy property. We introduce a generalized process by suitably time-changing a superposition of weighted space-fractional Poisson processes. This generalized process can be related to a specific subordinator for which it is possible to explicitly write the characterizing Lévy measure. Connections are highlighted to Prabhakar derivatives, specific convolution-type integral operators. Finally, we study the effect of introducing Prabhakar derivatives also in time.

A generalization of the space-fractional Poisson process and its connection to some Levy processes / Polito, Federico; Scalas, Enrico. - In: ELECTRONIC COMMUNICATIONS IN PROBABILITY. - ISSN 1083-589X. - 21:(2016), pp. 1-14. [10.1214/16-ecp4383]

A generalization of the space-fractional Poisson process and its connection to some Levy processes

Federico Polito
;
Enrico Scalas
2016

Abstract

The space-fractional Poisson process is a time-changed homogeneous Poisson process where the time change is an independent stable subordinator. In this paper, a further generalization is discussed that preserves the Lévy property. We introduce a generalized process by suitably time-changing a superposition of weighted space-fractional Poisson processes. This generalized process can be related to a specific subordinator for which it is possible to explicitly write the characterizing Lévy measure. Connections are highlighted to Prabhakar derivatives, specific convolution-type integral operators. Finally, we study the effect of introducing Prabhakar derivatives also in time.
2016
fractional point processes; Lévy processes; Prabhakar derivative; Prabhakar integral; subordination; time-change
01 Pubblicazione su rivista::01a Articolo in rivista
A generalization of the space-fractional Poisson process and its connection to some Levy processes / Polito, Federico; Scalas, Enrico. - In: ELECTRONIC COMMUNICATIONS IN PROBABILITY. - ISSN 1083-589X. - 21:(2016), pp. 1-14. [10.1214/16-ecp4383]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1668078
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