Article contents
On the long-range dependence of fractional Poisson and negative binomial processes
Part of:
Stochastic processes
Published online by Cambridge University Press: 09 December 2016
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).
MSC classification
Secondary:
60G55: Point processes
- Type
- Research Papers
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- Copyright © Applied Probability Trust 2016
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