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

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Dec 2016Embargo end date: 01 Jan 2016 India English Publisher:Cambridge University Press (CUP)Journal:Journal of Applied Probability, volume 53, pages 989-1,000 (issn: 0021-9002, eissn: 1475-6072,

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Authors: Aditya Maheshwari; P. Vellaisamy;

doi: 10.1017/jpr.2016.59 , 10.48550/arxiv.1601.05177

arXiv: 1601.05177

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

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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).

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India

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Keywords

fractional negative binomial process, Fractional Poisson Process, Probability (math.PR), Fractional processes, including fractional Brownian motion, Primary 60G22, Secondary 60G55, Long-Range Dependence, Long-range dependence, fractional Poisson process, Fractional Negative Binomial Process, long-range dependence, FOS: Mathematics, 60G22, 60G55, Point processes (e.g., Poisson, Cox, Hawkes processes), Mathematics - Probability

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