Polito, Federico and Scalas, Enrico (2016) A generalization of the space-fractional Poisson process and its connection to some Lévy processes. Electronic Communications in Probability, 21. pp. 20-34. ISSN 1083-589X

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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.

Item Type:	Article
Keywords:	fractional point processes; Lévy processes; Prabhakar integral; Prabhakar derivative; time-change subordination
Schools and Departments:	School of Mathematical and Physical Sciences > Mathematics
Subjects:	Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Related URLs:	Organisation
Depositing User:	Enrico Scalas
Date Deposited:	15 Mar 2016 08:13
Last Modified:	02 Jul 2019 20:05
URI:	http://sro.sussex.ac.uk/id/eprint/60035

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