The fractional non-homogeneous Poisson process

Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091, Scalas, E. and Trinh, M. 2017. The fractional non-homogeneous Poisson process. Statistics and Probablity Letters 120 , pp. 147-156. 10.1016/j.spl.2016.09.024

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Abstract

We introduce a non-homogeneous fractional Poisson process by replacing the time variable in the fractional Poisson process of renewal type with an appropriate function of time. We characterize the resulting process by deriving its non-local governing equation. We further compute the first and second moments of the process. Eventually, we derive the distribution of arrival times. Constant reference is made to previous known results in the homogeneous case and to how they can be derived from the specialization of the non-homogeneous process.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Fractional point processes; Lévy processes; Time-change; Subordination
Publisher:	Elsevier
ISSN:	0167-7152
Date of First Compliant Deposit:	6 October 2016
Date of Acceptance:	24 September 2016
Last Modified:	07 Nov 2023 07:22
URI:	https://orca.cardiff.ac.uk/id/eprint/95072

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