Comptes Rendus
no. 8
Probability Theory
Hölder conditions for the local times of multiscale fractional Brownian motion
[Temps local du mouvement Brownien fractionnaire à multi-échelle]

Présenté par : Marc Yor

Raby Guerbaz1
1 Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, 2390 Marrakesh, Morocco
Comptes Rendus. Mathématique, Volume 343 (2006) no. 8, pp. 515-518.

On étudie dans cette note les lois du logarithme itéré du temps local du mouvement Brownien fractionnaire à multi-échelle {Xρ(t),t⩾0}. On donne aussi la loi du logarithm itéré de type Chung pour Xρ, ceci implique que les résultats concernant le temps local sont optimales.

We establish estimates for the local and uniform moduli of continuity of local times of multiscale fractional Brownian motion {Xρ(t),t⩾0}. We also give Chung's form of the law of the iterated logarithm for Xρ, this proves that the results on local times are sharp up to multiplicative constant.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.09.026
Raby Guerbaz 1

1 Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, 2390 Marrakesh, Morocco 
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Raby Guerbaz. Hölder conditions for the local times of multiscale fractional Brownian motion. Comptes Rendus. Mathématique, Volume 343 (2006) no. 8, pp. 515-518. doi : 10.1016/j.crma.2006.09.026. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.09.026/

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