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Behavior of the Hermite sheet with respect to theHurst index

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  • Araya, Héctor
  • Tudor, Ciprian A.

Abstract

We consider a d-parameter Hermite process with Hurst index H=(H1,..,Hd)∈12,1d and we study its limit behavior in distribution when the Hurst parameters Hi,i=1,..,d (or a part of them) converge to 12 and/or 1. The limit obtained is Gaussian (when at least one parameter tends to 12) and non-Gaussian (when at least one-parameter tends to 1 and none converges to 12).

Suggested Citation

  • Araya, Héctor & Tudor, Ciprian A., 2019. "Behavior of the Hermite sheet with respect to theHurst index," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2582-2605.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:7:p:2582-2605
    DOI: 10.1016/j.spa.2018.07.017
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    References listed on IDEAS

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    1. Pipiras,Vladas & Taqqu,Murad S., 2017. "Long-Range Dependence and Self-Similarity," Cambridge Books, Cambridge University Press, number 9781107039469, November.
    2. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
    3. Bai, Shuyang & Taqqu, Murad S., 2014. "Structure of the third moment of the generalized Rosenblatt distribution," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 144-152.
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