The fractional non-homogeneous Poisson process

Leonenko, Nikolai, Scalas, Enrico and Trinh, Mailan (2017) The fractional non-homogeneous Poisson process. Statistics and Probability Letters, 120. pp. 147-156. ISSN 0167-7152

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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
Keywords: Fractional point processes; Lévy processes; Time-change; Subordination
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
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Depositing User: Enrico Scalas
Date Deposited: 28 Oct 2016 13:06
Last Modified: 06 Oct 2017 01:00
URI: http://sro.sussex.ac.uk/id/eprint/65113

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