Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Path transformations of first passage bridges

Auteur(s):

Code(s) de Classification MSC:

• 60J65 Brownian motion [See also 58J65]
• 60G09 Exchangeability
• 60G17 Sample path properties

Résumé: We define the first passage bridge from 0 to $\lambda$ as the Brownian motion on the time interval [0,1] conditioned to first hit $\lambda$ at time 1. We show that this process may be related to the Brownian bridge, the Bessel bridge or the Brownian excursion via some path transformations, the main one being an extension of Vervaat's transformation. We also propose an extension of these results to certain bridges with cyclically exchangeable increments.

Mots Clés: first passage bridge ; path transformation ; time of the minimum ; uniformly distributed time ; exchangeable increments

Date: 2003-07-02

Prépublication numéro: PMA-836