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Structure of the third moment of the generalized Rosenblatt distribution

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  • Bai, Shuyang
  • Taqqu, Murad S.

Abstract

The Rosenblatt distribution appears as limit in non-central limit theorems. The generalized Rosenblatt distribution is obtained by allowing different power exponents in the kernel that defines the usual Rosenblatt distribution. We derive an explicit formula for its third moment, correcting the one in Maejima and Tudor (2012) and Tudor (2013). Evaluating this formula numerically, we are able to confirm that the class of generalized Hermite processes is strictly richer than the class of Hermite processes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:94:y:2014:i:c:p:144-152
    DOI: 10.1016/j.spl.2014.07.012
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    References listed on IDEAS

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    1. Bai, Shuyang & Taqqu, Murad S., 2014. "Generalized Hermite processes, discrete chaos and limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1710-1739.
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    Cited by:

    1. 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.
    2. Ayache, Antoine, 2020. "Lower bound for local oscillations of Hermite processes," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4593-4607.

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