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

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

Moment problem for some convex functionals of Brownian motion and related processes


Code(s) de Classification MSC:

Résumé: This article provides a short and simple proof of the indeterminacy of \ $% A_{t}=\int_{0}^{t}\exp \left( \sigma B_{s}+\nu s\right) ds$, based on refinements of the Krein criteria recently obtained by A.G. Pakes ([15]) and on some elementary probability arguments. In fact, the indeterminacy of $% A_{t}$ is seen as a special case of a more general result about the indeterminacy of exponential functionals of continuous Gaussian processes. We also investigate some variants of this study, in particular when the exponential function is replaced by a wider class of convex functions and when $t$ is replaced by a random time.

Mots Clés: moments problem ; indeterminacy ; geometric Brownian motion ; exponential functional

Date: 2002-02-04

Prépublication numéro: PMA-706