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Fractional Poisson Fields

Author

Listed:
  • Nikolai Leonenko

    (Cardiff University)

  • Ely Merzbach

    (Bar-Ilan University)

Abstract

Using inverse subordinators and Mittag-Leffler functions, we present a new definition of a fractional Poisson process parametrized by points of the Euclidean space $\mathbb{R}_+^2$ . Some properties are given and, in particular, we prove a long-range dependence property.

Suggested Citation

  • Nikolai Leonenko & Ely Merzbach, 2015. "Fractional Poisson Fields," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 155-168, March.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:1:d:10.1007_s11009-013-9354-7
    DOI: 10.1007/s11009-013-9354-7
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    References listed on IDEAS

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    1. Orsingher, Enzo & Polito, Federico, 2012. "The space-fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 852-858.
    2. Wang, Xiao-Tian & Wen, Zhi-Xiong & Zhang, Shi-Ying, 2006. "Fractional Poisson process (II)," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 143-147.
    3. Wang, Xiao-Tian & Zhang, Shi-Ying & Fan, Shen, 2007. "Nonhomogeneous fractional Poisson processes," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 236-241.
    4. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag-Leffler Functions and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-51, May.
    5. Merzbach, Ely & Shaki, Yair Y., 2008. "Characterizations of multiparameter Cox and Poisson processes by the renewal property," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 637-642, April.
    6. Janczura, Joanna & Wyłomańska, Agnieszka, 2009. "Subdynamics of financial data from fractional Fokker-Planck equation," MPRA Paper 30649, University Library of Munich, Germany.
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    Cited by:

    1. Leonenko, Nikolai & Scalas, Enrico & Trinh, Mailan, 2017. "The fractional non-homogeneous Poisson process," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 147-156.
    2. A. Maheshwari & P. Vellaisamy, 2019. "Fractional Poisson Process Time-Changed by Lévy Subordinator and Its Inverse," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1278-1305, September.

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