Density estimates on a parabolic spde

Abstract

We consider a general class of parabolic spde's ∂uε t,x ∂t = ∂2uε t,x ∂x2 + ∂ ∂x g(uε t,x) + f(uε t,x) + εσ(uε t,x)W˙ t,x, with (t, x) ∈ [0, T] × [0, 1] and εW˙ t,x, ε > 0, a perturbed Gaussian space-time white noise. For (t, x) ∈ (0, T] × (0, 1) we prove the called Davies and Varadhan-L´eandre estimates of the density pε t,x of the solution uε t,x.