ON THE ASYMPTOTICS OF THE DENSITY IN PERTURBED SPDE'S WITH SPATIALLY CORRELATED NOISE

Abstract

We consider a general type of perturbed stochastic partial differential equations: [Formula: see text] with null initial conditions, [Formula: see text] a second-order partial differential operator and [Formula: see text] a Gaussian noise, white in time and correlated in space. It has been proved that there exists a smooth density [Formula: see text], t > 0, x ∈ ℝd, for the law of the solution of above-mentioned equation. Here, we find the Taylor expansion of this density [Formula: see text] on the diagonal.