[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
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