Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 21 (2016), paper no. 20, 14 pp.
A generalization of the space-fractional Poisson process and its connection to some Lévy processes
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.
Electron. Commun. Probab., Volume 21 (2016), paper no. 20, 14 pp.
Received: 24 June 2015
Accepted: 16 February 2016
First available in Project Euclid: 1 March 2016
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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