| 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:
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