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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60G44 Martingales with continuous parameter
- 60H07 Stochastic calculus of variations and the Malliavin calculus
- 60H20 Stochastic integral equations
- 60H30 Applications of stochastic analysis (to PDE, etc.)

**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