Excursions of the integral of the Brownian motion

Emmanuel Jacob (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

The integrated Brownian motion is sometimes known as the Langevin process. Lachal studied several excursion laws induced by the latter. Here we follow a different point of view developed by Pitman for general stationary processes. We first construct a stationary Langevin process and then determine explicitly its stationary excursion measure. This is then used to provide new descriptions of Itô's excursion measure of the Langevin process reflected at a completely inelastic boundary, which has been introduced recently by Bertoin.

Mots clés: Langevin process; stationary process; excursion measure; time-reversal; h-transform

Domaines: Probabilités [math.PR]

Emmanuel Jacob. Excursions of the integral of the Brownian motion. 2009. ⟨hal-00355172⟩