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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

A. Maheshwari  and
P. Vellaisamy
A. Maheshwari*
Affiliation:
Indian Institute of Technology Bombay
P. Vellaisamy*
Affiliation:
Indian Institute of Technology Bombay
*
* Postal address: Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India.
* Postal address: Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India.
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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).

Keywords

Long-range dependencefractional Poisson processfractional negative binomial process

MSC classification

Primary: 60G22: Fractional processes, including fractional Brownian motion
Secondary: 60G55: Point processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 4 , December 2016 , pp. 989 - 1000
Copyright
Copyright © Applied Probability Trust 2016 

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