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On the distribution of the Rosenblatt process

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  • Maejima, Makoto
  • Tudor, Ciprian A.

Abstract

We prove that the multivariate Rosenblatt distribution belongs to the Thorin class which is a subset of the class of selfdecomposable distributions. Using this fact we derive new properties of the Rosenblatt distribution.

Suggested Citation

  • Maejima, Makoto & Tudor, Ciprian A., 2013. "On the distribution of the Rosenblatt process," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1490-1495.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:6:p:1490-1495
    DOI: 10.1016/j.spl.2013.02.019
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    References listed on IDEAS

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    1. Albin, J. M. P., 1998. "A note on Rosenblatt distributions," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 83-91, September.
    2. 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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    Cited by:

    1. Mikko S. Pakkanen & Anthony Réveillac, 2014. "Functional limit theorems for generalized variations of the fractional Brownian sheet," CREATES Research Papers 2014-14, Department of Economics and Business Economics, Aarhus University.
    2. Upadhyay, Anjali & Kumar, Surendra, 2023. "The exponential nature and solvability of stochastic multi-term fractional differential inclusions with Clarke’s subdifferential," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. Tomasz Bojdecki & Luis G. Gorostiza & Anna Talarczyk, 2015. "From intersection local time to the Rosenblatt process," Journal of Theoretical Probability, Springer, vol. 28(3), pages 1227-1249, September.
    4. 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.
    5. Ghada AlNemer & Mohamed Hosny & Ramalingam Udhayakumar & Ahmed M. Elshenhab, 2024. "Existence and Hyers–Ulam Stability of Stochastic Delay Systems Governed by the Rosenblatt Process," Mathematics, MDPI, vol. 12(11), pages 1-15, June.
    6. Daw, Lara & Kerchev, George, 2023. "Fractal dimensions of the Rosenblatt process," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 544-571.
    7. Barakah Almarri & Xingtao Wang & Ahmed M. Elshenhab, 2022. "Controllability of Stochastic Delay Systems Driven by the Rosenblatt Process," Mathematics, MDPI, vol. 10(22), pages 1-20, November.
    8. 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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