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

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

Completely asymmetric LÚvy processes confined in a finite interval

Auteur(s):

Code(s) de Classification MSC:

RÚsumÚ: Consider a completely asymmetric LÚvy process which has absolutely continuous probabilities. By harmonic transform, we establish the existence of the LÚvy 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 ClÚs: LÚvy process; completely asymmetric; conditional law; $h$-transform; excursion measure

Date: 1999-03-23

Prépublication numéro: PMA-494