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

CNRS U.M.R. 7599
| ||

``Probabilités et Modèles Aléatoires''
| ||

**Auteur(s): **

**Code(s) de Classification MSC:**

- 60J30 Processes with independent increments

**Résumé:** Consider a completely asymmetric Lévy process which has absolutely continuous probabilities.
By harmonic transform, we establish the existence of the Lévy process conditioned to stay in
a finite interval, called the confined process (the confined Brownian motion is F.B.Knight's
Brownian taboo process). We show that the confined process is posive-recurrent and specify some useful
identities concerning its excursion measure away from a point. We investigate the rate of convergence of the
supremum process to the right-end point of the interval.

**Mots Clés:** *Lévy process; completely asymmetric; conditional law; $h$-transform; excursion measure*

**Date:** 1999-03-23

**Prépublication numéro:** *PMA-494*