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Fractional Poisson process (II)

Author

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  • Wang, Xiao-Tian
  • Wen, Zhi-Xiong
  • Zhang, Shi-Ying

Abstract

In this paper, we propose a stochastic process WH(t)(H∈(12,1)) which we call fractional Poisson process. The process WH(t) is self-similar in wide sense, displays long range dependence, and has more fatter tail than Gaussian process. In addition, it converges to fractional Brownian motion in distribution.

Suggested Citation

  • Wang, Xiao-Tian & Wen, Zhi-Xiong & Zhang, Shi-Ying, 2006. "Fractional Poisson process (II)," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 143-147.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:1:p:143-147
    DOI: 10.1016/j.chaos.2005.05.019
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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. Dexter O. Cahoy & Federico Polito, 2012. "Simulation and Estimation for the Fractional Yule Process," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 383-403, June.
    3. Araya, Héctor & Bahamonde, Natalia & Torres, Soledad & Viens, Frederi, 2019. "Donsker type theorem for fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 1-8.
    4. Nikolai Leonenko & Ely Merzbach, 2015. "Fractional Poisson Fields," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 155-168, March.
    5. Beghin, Luisa & Macci, Claudio, 2013. "Large deviations for fractional Poisson processes," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1193-1202.

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