Fractional non-homogeneous Poisson and Pólya-Aeppli processes of order k and beyond

Kadankova, Tetyana, Leonenko, Nikolai and Scalas, Enrico (2021) Fractional non-homogeneous Poisson and Pólya-Aeppli processes of order k and beyond. Communications in Statistics: Theory and Methods. ISSN 0361-0926

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Abstract

We introduce two classes of point processes: a fractional non-homogeneous Poisson process of order k and a fractional non-homogeneous Pólya-Aeppli process of order k: We characterize these processes by deriving their non-local governing equations. We further study the covariance structure of the processes and investigate the long-range dependence property.

Item Type: Article
Keywords: non-homogeneous fractional Poisson process of order k, non-homogeneous fractional P´olya-Aeppli process of order k, long range dependence, Caputo fractional derivative, a-stable L´evy subordinators, fractional integro-differential difference equations
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 20 Jul 2021 14:26
Last Modified: 16 Sep 2021 15:50
URI: http://sro.sussex.ac.uk/id/eprint/100624

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