Article (Scientific journals)
Different possible behaviors of wavelet leaders of the Brownian motion
Ayache, Antoine; Esser, Céline; Kleyntssens, Thomas
2019In Statistics and Probability Letters, 150, p. 54-60
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Keywords :
Brownian motion; Slow/fast/ordinary points; wavelet leaders; Modulus of continuity; Hölder spaces
Abstract :
[en] The aim of this paper is to prove that wavelet leaders allow to get very fine properties of the trajectories of the Brownian motion: more precisely, we show that there exist (at least) three different behaviors for the size of wavelet leaders of the Brownian motion. Furthermore, they correspond to the three well-known behaviors of its oscillations, namely to be ordinary, rapid and slow. Some links between the oscillations and the size of wavelet leaders at a given point are also given.
Disciplines :
Mathematics
Author, co-author :
Ayache, Antoine
Esser, Céline  ;  Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Kleyntssens, Thomas ;  Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Language :
English
Title :
Different possible behaviors of wavelet leaders of the Brownian motion
Publication date :
2019
Journal title :
Statistics and Probability Letters
ISSN :
0167-7152
Publisher :
Elsevier, Netherlands
Volume :
150
Pages :
54-60
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Available on ORBi :
since 27 January 2015

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