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

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

[img] PDF - Published Version
Available under License Creative Commons Attribution.

Download (261kB)

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:
Depositing User: Enrico Scalas
Date Deposited: 15 Mar 2016 08:13
Last Modified: 23 Mar 2017 17:56
URI: http://sro.sussex.ac.uk/id/eprint/60035

View download statistics for this item

📧 Request an update