Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Vervaat et LÚvy


Code(s) de Classification MSC:

RÚsumÚ: Vervaat has established a path transformation which gives a correspondence between the bridge and the excursion of a Brownian motion. Chaumont [C] has partly extended this correspondence to the stable case. Using the "General Theory of Processes", we show easily the Vervaat correspondence for LÚvy processes under the hypothesis of absolute continuity of the resolvent (which is called the (ACC) hypothesis of Sylvertein). Before establishing this correspondence, we give the appropriate definition of the bridge and the excursion for these processes by using potential theory. More precisely, we show that they are elementary transformations of two "Kuznetsov measures". We present this paper, in its content as well as in its spirit, as a tribute to the work of Paul-AndrÚ Meyer.

Mots ClÚs: LÚvy process ; Bridge ; Excursion

Date: 2004-03-05

Prépublication numéro: PMA-888