We propose a stochastic extension of deformation quantization on a Hilbert space. The Moyal product is defined in this context on the space of functionals belonging to all of the Sobolev spaces of the Malliavin calculus.
@article{hal-00002935,
author = {Dito, Giuseppe and Leandre, Remi},
title = {Produit de Moyal stochastique sur l'espace de Wiener},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00002935}
}
Dito, Giuseppe; Leandre, Remi. Produit de Moyal stochastique sur l'espace de Wiener. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00002935/