The paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue measure and continuously depends on the map. The results obtained are applied to the 2D Navier–Stokes equations perturbed by various random forces of low dimension.
Title: On finite-dimensional projections of distributions for solutions of randomly forced PDE's
Authors: A.A. Agrachev, S. Kuksin, A. Sarychev, A. Shirikyan
Journal title: Annales de l'IHP. Probabilites et statistiques