Cahn-Hilliard stochastic equation: Strict positivity of the density
Caroline Cardon-Weber · Stochastics and stochastics reports · 2002
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.