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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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Official URL: https://doi.org/10.1080/03610926.2021.1958228
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 |
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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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