Browse by: Author name - Classification - Keywords - Nature

2 matches found
VIII: 07, 37-77, LNM 381 (1974)
DUPUIS, Claire
Mesure de Hausdorff de la trajectoire de certains processus à accroissements indépendants et stationnaires (Independent increments)
The problem is to show that, for symmetric Lévy processes with small jumps and without a Brownian part, there exists a natural Hausdorff measure for which almost every path up to time $t$ has ``length'' exactly $t$. The case of Brownian motion had been known for a long time, the case of stable processes was settled by S.J.~Taylor (J. Math. Mech., 16, 1967) whose methods are generalized here
Keywords: Hausdorff measures, Lévy processes
Nature: Original
Retrieve article from Numdam
XIX: 27, 297-313, LNM 1123 (1985)
LE GALL, Jean-François
Sur la mesure de Hausdorff de la courbe brownienne (Brownian motion)
Previous results on the $h$-measure of the Brownian curve in $R^2$ or $R^3$ indexed by $t\in[0,1]$, by Cisielski-Taylor Trans. Amer. Math. Soc. 103 (1962) and Taylor Proc. Cambridge Philos. Soc. 60 (1964) are sharpened. The method uses the description à la Ray-Knight of the local times of Bessel processes
Comment: These Ray-Knight descriptions are useful ; they were later used in questions not related to Hausdorff measures. See for instance Biane-Yor, Ann. I.H.P. 23 (1987), Yor, Ann. I.H.P. 27 (1991)
Keywords: Hausdorff measures, Brownian motion, Bessel processes, Ray-Knight theorems
Nature: Original
Retrieve article from Numdam