Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional non-homogeneous Poisson and P\'olya-Aeppli processes of order
  $k$ and beyond   We introduce two non-homogeneous processes: a fractional non-homogeneous
Poisson process of order $k$ and and a fractional non-homogeneous
P\'olya-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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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: q-fin