364 research outputs found
On the Long-range Dependence of Fractional Poisson and Negative Binomial Processes
We study the long-range dependence (LRD) of the increments of the fractional
Poisson process (FPP), the fractional negative binomial process (FNBP) and the
increments of the FNBP. We first point out an error in the proof of Theorem 1
of Biard and Saussereau (2014) and prove that the increments of the FPP has
indeed the short-range dependence (SRD) property, when the fractional index
satisfies . We also establish that the FNBP has
the LRD property, while the increments of the FNBP possesses the SRD property.Comment: 17 page
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