Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Some consequences of the cyclic exchangeability property for exponential functionals of Lévy processes

Auteur(s):

Code(s) de Classification MSC:

• 60J30 Processes with independent increments
• 60J20 Applications of discrete Markov processes (social mobility, learning theory, industrial processes, etc.), See Also {90B30, 92H10, 92H35, 92J40}

Résumé: In this paper we derive some distributional properties of Lévy 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 Clés: Cyclic exchangeability ; Lévy and Brownian bridges ; exponential functionals

Date: 2000-03-15

Prépublication numéro: PMA-574