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

Tetyana Kadankova; Nikolai Leonenko; Enrico Scalas

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arXiv · 2008.09421

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 non-homogeneous processes: a fractional non-homogeneous Poisson process of order $k$ and 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.

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Tetyana Kadankova, Nikolai Leonenko, Enrico Scalas. 2021-05-03. Fractional non-homogeneous Poisson and Pólya-Aeppli processes of order $k$ and beyond. https://arxiv.org/abs/2008.09421

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