Regular Densities of Invariant Measures in Hilbert Spaces

We consider a nonlinear differential stochastical equation in a Hilbert space, that is, a Lipschitzian perturbation of a linear equation. We prove that, under suitable hypotheses, both equations have invariant measures μ and μ₀ respectively and that μ is absolutely continuous with respect to μ₀. We also give several regularity results on the density dμ/dμ₀.