On the long-range dependence of fractional Poisson and negative binomial processes
TLDR
In this article, the short-range dependence (SRD) property of the increments of the fractional Poisson process was discussed, and it was shown that fractional negative binomial process (FNBP) has the same property.Abstract:
We discuss the short-range dependence (SRD) property of the increments of the fractional Poisson process, called the fractional Poissonian noise. We also establish that the fractional negative binomial process (FNBP) has the long-range dependence (LRD) property, while the increments of the FNBP have the SRD property. Our definitions of the SRD/LRD properties are similar to those for a stationary process and different from those recently used in Biard and Saussereau (2014).read more
Citations
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Fractional Poisson Process Time-Changed by Lévy Subordinator and Its Inverse
TL;DR: In this paper, the authors studied the fractional Poisson process (FPP) time-changed by an independent Levy subordinator and the inverse of the Levy subordinators, which they call TCFPP-I and TC FPP-II, respectively.
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A fractional counting process and its connection with the Poisson process
TL;DR: In this article, a fractional counting process with jumps of amplitude 1,2,...,k, withk∈N, whose probabilistic ability to satisfy a suitablesystemoffractionaldifference-differential equations is considered.
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Limit theorems for the fractional non-homogeneous Poisson process
TL;DR: Both finite-dimensional and functional limit theorems for the fractional nonhomogeneous Poisson process and the fractionsal compound Poissonprocess are given.
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Time-changed Poisson processes of order k
TL;DR: In this article, the Poisson process of order k (PPoK) time-changed with an independent Levy subordinator and its inverse was studied, which they called TCPPoK-I and TCPPoK-II.
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Skellam type processes of order K and beyond
TL;DR: In this article, the Skellam process of order k and its running average was introduced and the marginal probabilities, Levy measures, governing difference-differential equations of the introduced processes were derived.
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