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On the Long-Range Dependence of Mixed Fractional Poisson Process

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  • K. K. Kataria

    (Indian Institute of Technology Bhilai)

  • M. Khandakar

    (Indian Institute of Technology Bhilai)

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.

Suggested Citation

  • K. K. Kataria & M. Khandakar, 2021. "On the Long-Range Dependence of Mixed Fractional Poisson Process," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1607-1622, September.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:3:d:10.1007_s10959-020-01015-y
    DOI: 10.1007/s10959-020-01015-y
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    References listed on IDEAS

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    1. L. Beghin & P. Vellaisamy, 2018. "Space-Fractional Versions of the Negative Binomial and Polya-Type Processes," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 463-485, June.
    2. Beghin, L., 2012. "Random-time processes governed by differential equations of fractional distributed order," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1314-1327.
    3. Mark Veillette & Murad S. Taqqu, 2010. "Numerical Computation of First-Passage Times of Increasing Lévy Processes," Methodology and Computing in Applied Probability, Springer, vol. 12(4), pages 695-729, December.
    4. Orsingher, Enzo & Polito, Federico, 2012. "The space-fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 852-858.
    5. Beghin, Luisa & Macci, Claudio, 2013. "Large deviations for fractional Poisson processes," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1193-1202.
    6. Veillette, Mark & Taqqu, Murad S., 2010. "Using differential equations to obtain joint moments of first-passage times of increasing Lévy processes," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 697-705, April.
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