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Theory of Probability and Mathematical Statistics

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Limit behavior of the Rosenblatt Ornstein-Uhlenbeck process with respect to the Hurst index


Authors: M. Slaoui and C. A. Tudor
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 98 (2018).
Journal: Theor. Probability and Math. Statist. 98 (2019), 183-198
MSC (2010): Primary 60H05, 60H15, 60G22
DOI: https://doi.org/10.1090/tpms/1070
Published electronically: August 19, 2019
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Abstract: We study the convergence in distribution, as $ H\to \frac {1}{2}$ and as $ H\to 1$, of the integral $ \int _{\mathbb{R}} f(u)\,dZ^{H}(u) $, where $ Z^{H}$ is a Rosenblatt process with self-similarity index $ H\in \left (\frac {1}{2}, 1\right ) $ and $ f$ is a suitable deterministic function. We focus our analysis on the case of the Rosenblatt Ornstein-Uhlenbeck process, which is the solution of the Langevin equation driven by the Rosenblatt process.


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Additional Information

M. Slaoui
Affiliation: Laboratoire Paul Painlevé, Université de Lille 1, F-59655 Villeneuve d’Ascq, France
Email: meryem.slaoui@math.univ-lille1.fr

C. A. Tudor
Affiliation: Laboratoire Paul Painlevé, Université de Lille 1, F-59655 Villeneuve d’Ascq, France, and ISMMA, Romanian Academy, Romania
Email: tudor@math.univ-lille1.fr

DOI: https://doi.org/10.1090/tpms/1070
Keywords: Wiener chaos, Rosenblatt process, cumulants, Hurst parameter
Received by editor(s): January 8, 2018
Published electronically: August 19, 2019
Article copyright: © Copyright 2019 American Mathematical Society