On the long-range dependence of fractional Poisson and negative binomial processes. (9th December 2016)

• Record Type: Journal Article
• Authors: Maheshwari, A.; Vellaisamy, P.
• Is Part Of: Journal of applied probability. Volume 53:Number 4(2016)
• Page Start: 989
• Page End: 1000
• Publication Date: 2016-12-09
• Subjects: Long-range dependence, -- fractional Poisson process, -- fractional negative binomial process; Primary 60G22, -- Secondary 60G55; 519.2
• DOI: 10.1017/jpr.2016.59
• Languages: English
• ISSNs: 0021-9002

Abstract

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).