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

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

Pinning class of the Wiener measure by a functional : Related martingales and invariance properties


Code(s) de Classification MSC:

Résumé: For a given functional $Y$ on the path space, we define the pinning class of the Wiener measure as the class of probabilities which admit the same conditioning given $Y$ as the Wiener measure. Using stochastic analysis and the theory of initial enlargement of filtration, we study the transformations (not necessarily adapted) which preserve this class. We prove, in this non Markov setting, a stochastic Newton equation and a stochastic Noether theorem. We conclude the paper with some non canonical representations of Brownian motion, closely related to our study.

Mots Clés: Conditioned stochastic differential equation ; Initial enlargement of filtrations ; Newton's martingale ; Noether's stochastic theorem ; Stochastic analysis ; Symmetries in stochastic calculus

Date: 2002-06-13

Prépublication numéro: PMA-739

Pdf file : PMA-739.pdf