Stability for stochastic partial differential equations with Dirichlet white-noise boundary conditions

In this paper we study the long-time behaviour a stochastic parabolic equation perturbed through the boundary; the perturbation is represented by a nonhomogeneous Dirichlet boundary condition of white-noise type. The existence of the solution for an equation of this kind was the object of a previous paper of the same authors. The estimates proved therein allow to study the asymptotic properties of the solution; we show that there exists a unique invariant measure that is exponentially mean square stable.