La mesure de Hausdorff des trajectoires du mouvement brownien à plusieurs paramètres (Hausdorff measure for the range of a time- multidimensional Brownian motion process). (French) Zbl 0584.60063

Goldman, André

C. R. Acad. Sci., Paris, Sér. I 300, 643-645 (1985).

The function \(\phi (x)=x^{2p}\ln \ln x^{-1}\) is shown to be an exact Hausdorff measure function for the range of a transient Lévy Brownian motion process with multidimensional time. This result settles a question by P. Lévy [Rend. Mat. Appl., V. Ser. 22, 24-101 (1963; Zbl 0121.191) and Research papers Statist., Festschr. J. Neyman, 189-223 (1966)]. The main tool is a projection lemma (of independent interest) based on McKean’s decomposition of Brownian motion.

MSC:

60G60	Random fields
60J65	Brownian motion

Keywords:

Hausdorff measure; projection lemma; decomposition of Brownian motion

Citations:

Zbl 0294.60061; Zbl 0121.191