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

### Rogers and Walsh's integral representation of martingales in a stochastic flow

Auteur(s):

Code(s) de Classification MSC:

• 60H05 Stochastic integrals
• 60G44 Martingales with continuous parameter

Résumé: Bass and Burdzy [1] recently studied a stochastic flow of ${\cal C}^1$-homeomorphisms on $\r$, associated to a natural generalization of a Brownian motion with drift. We show that all martingales in this flow admit an area integral representation by using the method developped by Rogers and Walsh [12] in the case of the Brownian excursion filtration. This also gives another representation of the square integrable variables in the Brownian field.

Mots Clés: Integral representation ; flow ; area integral

Date: 2001-06-15

Prépublication numéro: PMA-669

Postscript file : PMA-669.ps