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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 44A60 Moment problems
- 60J60 Diffusion processes, See also {58G32}

**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*