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2016 A generalization of the space-fractional Poisson process and its connection to some Lévy processes
Federico Polito, Enrico Scalas
Electron. Commun. Probab. 21: 1-14 (2016). DOI: 10.1214/16-ECP4383

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.

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Federico Polito. Enrico Scalas. "A generalization of the space-fractional Poisson process and its connection to some Lévy processes." Electron. Commun. Probab. 21 1 - 14, 2016. https://doi.org/10.1214/16-ECP4383

Information

Received: 24 June 2015; Accepted: 16 February 2016; Published: 2016
First available in Project Euclid: 1 March 2016

zbMATH: 1338.60129
MathSciNet: MR3485389
Digital Object Identifier: 10.1214/16-ECP4383

Subjects:
Primary: 26A33, 60G22, 60G51

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