Excursions of the integral of the Brownian motion

Details Excursions of the integral of the Brownian motion Excursions of the integral of the Brownian motion

2009-01-22

arxiv.org/abs/0901.3464v2

Mathematics

Probability

In this second version, some consequent changes of notations and presentation. The space we work on for Proposition 2 and Theo

Scientific paper

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.

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