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

Esser, Céline; Loosveldt, Laurent

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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

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https://hdl.handle.net/2268/293130

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Keywords :

Mathematics - Probability; Mathematics - Functional Analysis; 42C40 26A16 60G15 60G22 60G17

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. We also show that this property is satisfied for a multifractal extension of Gaussian wavelet series. Finally, we remark that the existence of slow points is specific to these functions.

Disciplines :

Mathematics

Author, co-author :

Esser, Céline ; Université de Liège - ULiège > Département de mathématique > Analyse mathématique et ses interactions avec la théorie des probabilités

Loosveldt, Laurent ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Language :

English

Title :

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

Publication date :

2022

Journal title :

ALEA: Latin American Journal of Probability and Mathematical Statistics

eISSN :

1980-0436

Publisher :

Instituto Nacional de Matematica Pura e Aplicada, Brazil

Volume :

Pages :

1471–1495

Peer reviewed :

Peer Reviewed verified by ORBi

Commentary :

33 pages

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since 08 July 2022

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