Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**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*