Excursions of the integral of the Brownian motion

E. 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 Ito's excursion measure of the Langevin process reflected at a completely inelastic boundary, which has been introduced recently by Bertoin.

Domaines: Probabilités [math.PR]

E. Jacob. Excursions of the integral of the Brownian motion. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2010, 46 (3), pp.869-887. ⟨10.1214/09-AIHP322⟩. ⟨hal-00518149⟩