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Nonhomogeneous fractional Poisson processes

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  • Wang, Xiao-Tian
  • Zhang, Shi-Ying
  • Fan, Shen

Abstract

In this paper, we propose a class of non-Gaussian stationary increment processes, named nonhomogeneous fractional Poisson processes WH(j)(t), which permit the study of the effects of long-range dependance in a large number of fields including quantum physics and finance. The processes WH(j)(t) are self-similar in a wide sense, exhibit more fatter tail than Gaussian processes, and converge to the Gaussian processes in distribution in some cases. In addition, we also show that the intensity function λ(t) strongly influences the existence of the highest finite moment of WH(j)(t) and the behaviour of the tail probability of WH(j)(t).

Suggested Citation

  • Wang, Xiao-Tian & Zhang, Shi-Ying & Fan, Shen, 2007. "Nonhomogeneous fractional Poisson processes," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 236-241.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:1:p:236-241
    DOI: 10.1016/j.chaos.2005.09.063
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    Cited by:

    1. 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.
    2. Leonenko, Nikolai & Scalas, Enrico & Trinh, Mailan, 2017. "The fractional non-homogeneous Poisson process," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 147-156.
    3. Nikolai Leonenko & Ely Merzbach, 2015. "Fractional Poisson Fields," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 155-168, March.
    4. 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.

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