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:**

- 60H07 Stochastic calculus of variations and the Malliavin calculus
- 60H15 Stochastic partial differential equations, See also {35R60}
- 35R60 Partial differential equations with randomness, See Also {

**Résumé:** This paper deals with the Cahn-Hilliard stochastic equation driven
by a space-time white noise with a non-linear diffusion
coefficient. Using new lower estimate of the kernel, we prove the
"local" existence of the density without non-degeneracy condition in a case
of Hölder continuous trajectories, and we show that the density of any vector is lower bounded by a strictly positive
continuous function under a non-degeneracy condition.

**Mots Clés:** *Cahn-Hilliard equation ; SPDEs ; Stochastic calculus of variations*

**Date:** 2000-03-17

**Prépublication numéro:** *PMA-576*

** Postcript file : PMA-576.ps
**