Wavelet methods to study the pointwise regularity of the generalized Rosenblatt process

Daw, Lara; Loosveldt, Laurent

doi:10.1214/22-EJP878

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Wavelet methods to study the pointwise regularity of the generalized Rosenblatt process

Daw, Lara; Loosveldt, Laurent

2022 • In Electronic Journal of Probability, 27, p. 1-45

Peer Reviewed verified by ORBi

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https://hdl.handle.net/10993/50566

DOI
10.1214/22-EJP878

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Keywords :

Wiener chaos,; Rosenblatt process,; Wavelet series,; Random Series,; slow/ordinary/rapid points,; modulus of continuity

Abstract :

[en] 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.

Disciplines :

Mathematics

Author, co-author :

Daw, Lara ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)

Loosveldt, Laurent ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)

External co-authors :

Language :

English

Title :

Wavelet methods to study the pointwise regularity of the generalized Rosenblatt process

Publication date :

November 2022

Journal title :

Electronic Journal of Probability

ISSN :

1083-6489

Publisher :

Institute of Mathematical Statistics, Beachwood, United States - Ohio

Volume :

Pages :

1-45

Peer reviewed :

Peer Reviewed verified by ORBi

FnR Project :

FNR12582675 - Approximation Of Gaussian Functionals, 2018 (01/09/2019-31/08/2022) - Ivan Nourdin

Funders :

FNR - Fonds National de la Recherche [LU]

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since 11 March 2022

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