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

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

Properties of perpetual integral functionals of Brownian motion with drift

Auteur(s):

Code(s) de Classification MSC:

Résumé: In this paper we study integrability properties of the random variables $$I_\infty(f):=\int_0^\infty f(B^{(\mu)}_t)\, dt, $$ where $\{B^{(\mu)}_t:t\geq~0\}$ is a Brownian motion with drift $\mu>0$ and $f$ is a non-negative, Borel measurable function. In particular, we find conditions under which $ I_\infty(f)$ (i) is finite a.s., (ii) has all the moments, (iii) has some exponential moments, (iv) has bounded potential.

Mots Clés: Local time ; Green function ; Kac's moment formula ; Khas'minskii's lemma ; last exit time

Date: 2003-09-18

Prépublication numéro: PMA-845