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

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

Duality formula for the bridges of a Brownian diffusion. Application to gradient drifts

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Code(s) de Classification MSC:

Résumé: In this paper we consider families of time Markov fields (or reciprocal classes) which have the same bridges as a Brownian diffusion. We characterize each class as the set of solutions of an integration by parts formula on the space of continuous paths $C([0;1];{\R}^d)$. Our techniques provide a characterization of gradient diffusions by a duality formula and, in case of reversibility, a generalization of a result of Kolmogorov.

Mots Clés: reciprocal processes ; stochastic bridge ; mixture of bridges ; integration by parts formula ; Malliavin calculus ; entropy ; time reversal ; reversible process

Date: 2002-12-20

Prépublication numéro: PMA-784