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Donsker type theorem for fractional Poisson process

Author

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  • Araya, Héctor
  • Bahamonde, Natalia
  • Torres, Soledad
  • Viens, Frederi

Abstract

In this paper we study a Donsker type theorem for the fractional Poisson process (fPp). We present the random walk discretization and its associated convergence theorem in the Skorohod topology. Simulation results are also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:150:y:2019:i:c:p:1-8
    DOI: 10.1016/j.spl.2019.01.036
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    References listed on IDEAS

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    1. Jost, Céline, 2006. "Transformation formulas for fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1341-1357, October.
    2. Wang, Xiao-Tian & Zhang, Shi-Ying & Fan, Shen, 2007. "Nonhomogeneous fractional Poisson processes," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 236-241.
    3. Stefan Rostek, 2009. "Option Pricing in Fractional Brownian Markets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-00331-8, October.
    4. Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.
    5. Wang, Xiao-Tian & Wen, Zhi-Xiong & Zhang, Shi-Ying, 2006. "Fractional Poisson process (II)," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 143-147.
    6. Hongshuai Dai, 2016. "Random walks and subfractional Brownian motion," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(10), pages 2834-2841, May.
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    Cited by:

    1. Wang, XiaoTian & Yang, ZiJian & Cao, PiYao & Wang, ShiLin, 2021. "The closed-form option pricing formulas under the sub-fractional Poisson volatility models," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).

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