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A note on Rosenblatt distributions

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  • Albin, J. M. P.

Abstract

Rosenblatt processes are functional limits in non-central limit theorems for strongly dependent Gaussian sequences. Using local limit techniques we show that their marginal distributions belong to the Type I domain of attraction of extremes. This in turn makes it possible to obtain bounds on local extremes for Rosenblatt processes.

Suggested Citation

  • Albin, J. M. P., 1998. "A note on Rosenblatt distributions," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 83-91, September.
    • Handle: RePEc:eee:stapro:v:40:y:1998:i:1:p:83-91
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    References listed on IDEAS

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    1. Albin, J. M. P., 1992. "Extremes and crossings for differentiable stationary processes with application to Gaussian processes in m and Hilbert space," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 119-147, August.
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    Cited by:

    1. Maejima, Makoto & Tudor, Ciprian A., 2013. "On the distribution of the Rosenblatt process," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1490-1495.
    2. Chen, Zhenlong & Xu, Lin & Zhu, Dongjin, 2015. "Generalized continuous time random walks and Hermite processes," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 44-53.
    3. Čoupek, Petr & Duncan, Tyrone E. & Pasik-Duncan, Bozenna, 2022. "A stochastic calculus for Rosenblatt processes," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 853-885.
    4. Pipiras, Vladas & Taqqu, Murad S., 2010. "Regularization and integral representations of Hermite processes," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 2014-2023, December.

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    1. Albin, J. M. P., 2000. "Extremes and upcrossing intensities for P-differentiable stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 199-234, June.
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