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.
Fractional non-homogeneous Poisson and Pólya-Aeppli processes of order $k$ and beyond / Kadankova, T.; Leonenko, N.; Scalas, E.. - In: COMMUNICATIONS IN STATISTICS, THEORY AND METHODS. - ISSN 1532-415X. - (2021), pp. 1-20. [10.1080/03610926.2021.1958228]
Fractional non-homogeneous Poisson and Pólya-Aeppli processes of order $k$ and beyond
Scalas E.
2021
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.File allegati a questo prodotto
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