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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

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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

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 (

Keywords: Hausdorff measures, Lévy processes

Nature: Original

Retrieve article from Numdam

XIX: 27, 297-313, LNM 1123 (1985)

Sur la mesure de Hausdorff de la courbe brownienne (Brownian motion)

Previous results on the $h$-measure of the Brownian curve in $

Comment: These Ray-Knight descriptions are useful ; they were later used in questions not related to Hausdorff measures. See for instance Biane-Yor,

Keywords: Hausdorff measures, Brownian motion, Bessel processes, Ray-Knight theorems

Nature: Original

Retrieve article from Numdam