On the long-range dependence of fractional Poisson and negative binomial processes

On the long-range dependence of fractional Poisson and negative binomial processes

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...

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Bibliographic Details
Published in:Journal of applied probability Vol. 53; no. 4; pp. 989 - 1000
Main Authors: Maheshwari, A., Vellaisamy, P.
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01-12-2016
Applied Probability Trust
Subjects:
Binomial distribution
Binomials
Dependence
Fractions
Noise
Poisson density functions
Poisson distribution
Poisson process
Research Papers
Stochastic processes
Studies
fractional Poisson process
Long-range dependence
Secondary 60G55
Primary 60G22
fractional negative binomial process
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Summary: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).
Bibliography:ObjectType-Article-1
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ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2016.59