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

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

Some consequences of the cyclic exchangeability property for exponential functionals of LÚvy processes


Code(s) de Classification MSC:

RÚsumÚ: In this paper we derive some distributional properties of LÚvy processes and bridges from their cyclic exchangeability property. We first describe the $\sigma$-field which is invariant under the cyclic transformations. Then, by conditioning on this $\sigma$-field, we obtain information about the laws of many Brownian functionals, such as exponential functionals, quantiles and local time.

Mots ClÚs: Cyclic exchangeability ; LÚvy and Brownian bridges ; exponential functionals

Date: 2000-03-15

Prépublication numéro: PMA-574