Title :

Different possible behaviors of wavelet leaders of the Brownian motion

Author(s) :

Ayache, Antoine [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Esser, Céline [Auteur]
Université de Liège
Kleyntssens, Thomas [Auteur]

Journal title :

Statistics and Probability Letters

Pages :

54-60

Publisher :

Elsevier

Publication date :

2019

ISSN :

0167-7152

English keyword(s) :

Brownian motion
slow points
fast points
ordinary points
wavelet leaders
modulus of continuity
Hölder spaces

HAL domain(s) :

Mathématiques [math]

English 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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL