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.
@article{1281100402,
author = {Jacob, Emmanuel},
title = {Excursions of the integral of the Brownian motion},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {46},
number = {1},
year = {2010},
pages = { 869-887},
language = {en},
url = {http://dml.mathdoc.fr/item/1281100402}
}
Jacob, Emmanuel. Excursions of the integral of the Brownian motion. Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, pp. 869-887. http://gdmltest.u-ga.fr/item/1281100402/