Electronic Communications in Probability

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

Federico Polito and Enrico Scalas

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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.

Article information

Source
Electron. Commun. Probab., Volume 21 (2016), paper no. 20, 14 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1456840981

Digital Object Identifier
doi:10.1214/16-ECP4383

Mathematical Reviews number (MathSciNet)
MR3485389

Zentralblatt MATH identifier
1338.60129

Subjects
Primary: 60G51: Processes with independent increments; Lévy processes 60G22: Fractional processes, including fractional Brownian motion 26A33: Fractional derivatives and integrals

Keywords
fractional point processes Lévy processes Prabhakar integral Prabhakar derivative time-change subordination

Rights
Creative Commons Attribution 4.0 International License.

Citation

Polito, Federico; Scalas, Enrico. A generalization of the space-fractional Poisson process and its connection to some Lévy processes. Electron. Commun. Probab. 21 (2016), paper no. 20, 14 pp. doi:10.1214/16-ECP4383. https://projecteuclid.org/euclid.ecp/1456840981


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