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

random series; Rosenblatt process; slow/ordinary/rapid points, modulus of continuity; wavelet series; Wiener chaos; Statistics and Probability; Statistics, Probability and Uncertainty

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, Department of Mathematics (DMATH), Esch-sur-Alzette, Luxembourg

Loosveldt, Laurent ; Université de Liège - ULiège > Mathematics ; University of Luxembourg, Department of Mathematics (DMATH), Esch-sur-Alzette, Luxembourg

Language :

English

Title :

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

Publication date :

2022

Journal title :

Electronic Journal of Probability

eISSN :

1083-6489

Publisher :

Institute of Mathematical Statistics

Volume :

Issue :

none

Peer reviewed :

Peer Reviewed verified by ORBi

Funding text :

FNR OPEN grant APOGEe at University of Luxembourg

Available on ORBi :

since 05 September 2023

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