On the Long-Range Dependence of Mixed Fractional Poisson Process

K. K. Kataria () and M. Khandakar ()
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K. K. Kataria: Indian Institute of Technology Bhilai
M. Khandakar: Indian Institute of Technology Bhilai

Journal of Theoretical Probability, 2021, vol. 34, issue 3, 1607-1622

Abstract: Abstract In this paper, we show that the mixed fractional Poisson process (MFPP) exhibits the long-range dependence property. It is proved by establishing an asymptotic result for the covariance of inverse mixed stable subordinator. Also, it is shown that the increment process of the MFPP, namely the mixed fractional Poissonian noise, has the short-range dependence property.

Keywords: Mixed fractional Poisson process; Mixed fractional Poissonian noise; LRD property; SRD property; 60G22; 60G55 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-01015-y

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