Abstract
We identify three types of pointwise behaviour in the regularity of the (generalized) Rosenblatt process. This extends to a non Gaussian setting previous results known for the (fractional) Brownian motion. On this purpose, fine bounds on the increments of the Rosenblatt process are needed. Our analysis is essentially based on various wavelet methods.
Funding Statement
Both authors are supported by the FNR OPEN grant APOGEe at University of Luxembourg.
Acknowledgments
The authors thank Céline Esser from University of Liège, Ivan Nourdin from University of Luxembourg and Stéphane Seuret from University Paris Est Créteil for fruitful discussions and valuable advices.
The authors are grateful to two referees for their valuable comments and suggestions which helped to improve the presentation of the paper.
Version Information
The authors updated reference [18] on 2022-11-30.
Citation
Lara Daw. Laurent Loosveldt. "Wavelet methods to study the pointwise regularity of the generalized Rosenblatt process." Electron. J. Probab. 27 1 - 45, 2022. https://doi.org/10.1214/22-EJP878
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