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

Tetyana Kadankova, Nikolai Leonenko and Enrico Scalas

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 8, 2682-2701

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.

Date: 2023
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DOI: 10.1080/03610926.2021.1958228

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