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

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

On the entire moments of self-similar Markov processes and exponential functionals of LÚvy processes

Auteur(s):

Code(s) de Classification MSC:

RÚsumÚ: We compute the positive entire moments of certain self-similar Markov processes evaluated at a fixed time, and the negative entire moments of the exponential functional $I$ of certain L\'evy processes. When the L\'evy process has no positive jumps, this determines the aforementioned distributions and yields several interesting identities in law. The case of the Poisson process yields yet another simple example showing that the log-normal distribution is moment-indeterminate.

Mots ClÚs: LÚvy process ; exponential functional ; classical moment problem

Date: 2001-12-14

Prépublication numéro: PMA-702