Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Level sets of multiparameter Brownian motions

Auteur(s):

Code(s) de Classification MSC:

• 60G60 Random fields
• 60G15 Gaussian processes
• 60G17 Sample path properties

Résumé: We use Girsanov's theorem to establish a conjecture of Khoshnevisan, Xiao and Zhong that $\phi(r) = r^{N-d/2} (\log \log (\frac{1}{r}))^{d/2}$ is the exact Hausdorff measure function for the zero level set of an $N$-parameter $d$-dimensional additive Brownian motion. We extend this result to a natural multiparameter version of Taylor and Wendel's theorem on the relationship between Brownian local time and the Hausdorff $\phi$-measure of the zero set.

Mots Clés: Local times ; Hausdorff measure ; Level sets ; Additive Brownian motion

Date: 2003-11-25

Prépublication numéro: PMA-867