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

2016/12/01 by A. Maheshwari, Aditya Maheshwari, P. Vellaisamy · 52 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Bayesian Methods and Mixture Models #Binomial (polynomial) #Financial Risk and Volatility Modeling #Mathematics #Negative binomial distribution #Physics #Poisson distribution #Poisson process #Property (philosophy) #Range (aeronautics) #Statistical Distribution Estimation and Applications #Statistical physics #Statistics

paper · doi:10.1017/jpr.2016.59

published in Journal of Applied Probability 53(4), 989-1000 (Cambridge University Press)

openalex publication_date 2016/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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).

Citations

• Fractional Poisson Process: Long-Range Dependence and Applications in Ruin Theory

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• Skellam Type Processes of Order k and Beyond. [europepmc]

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