Slow, ordinary and rapid points for Gaussian Wavelets Series and application to Fractional Brownian Motions

Esser, Céline; LOOSVELDT, Laurent

doi:10.30757/ALEA.v19-59

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Slow, ordinary and rapid points for Gaussian Wavelets Series and application to Fractional Brownian Motions

Esser, Céline; LOOSVELDT, Laurent

2022 • In ALEA: Latin American Journal of Probability and Mathematical Statistics, 19, p. 1471-1495

Peer Reviewed verified by ORBi

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https://hdl.handle.net/10993/53159

DOI
10.30757/ALEA.v19-59

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Keywords :

Random Wavelets Series,; Fractional Brownian motion; modulus of continuity; slow/ordinary/rapid points

Abstract :

[en] We study the Hölderian regularity of Gaussian wavelets series and show that they display, almost surely, three types of points: slow, ordinary and rapid. In particular, this fact holds for the Fractional Brownian Motion. Finally, we remark that the existence of slow points is specific to these functions.

Disciplines :

Mathematics

Author, co-author :

Esser, Céline; Université de Liège - ULg > UR Mathematics

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

External co-authors :

yes

Language :

English

Title :

Slow, ordinary and rapid points for Gaussian Wavelets Series and application to Fractional Brownian Motions

Publication date :

November 2022

Journal title :

ALEA: Latin American Journal of Probability and Mathematical Statistics

eISSN :

1980-0436

Publisher :

Instituto Nacional de Matematica Pura e Aplicada, Rio de Janeiro, Brazil

Volume :

Pages :

1471-1495

Peer reviewed :

Peer Reviewed verified by ORBi

FnR Project :

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

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since 15 December 2022

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