2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120744The paper analyses a model in surface growth, where uniqueness of weak solutions seems to be out of reach. We provide the existence of a weak martingale solution satisfying energy inequalities and having the Markov property. Furthermore, under non-degeneracy conditions on the noise, we establish that any such solution is strong Feller and has a unique invariant measure.33 pages, 1 figureProbabilityMathematical Physics60H15; 35Q99, 35R60, 60H30text