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

Tetyana Kadankova, Nikolai Leonenko, Enrico Scalas

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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.
Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalCommunications in Statistics - Theory and Methods
DOIs
Publication statusPublished - 2021

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