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

Author

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  • Tetyana Kadankova
  • Nikolai Leonenko
  • Enrico Scalas

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.

Suggested Citation

  • Tetyana Kadankova & Nikolai Leonenko & Enrico Scalas, 2023. "Fractional non-homogeneous Poisson and Pólya-Aeppli processes of order k and beyond," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(8), pages 2682-2701, April.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:8:p:2682-2701
    DOI: 10.1080/03610926.2021.1958228
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