Existence of Invariant Measures for Reflected SPDEs

Abstract

In this article, we close a gap in the literature by proving existence of invariant measures for reflected SPDEs with only one reflecting barrier. This is done by arguing that the sequence (u(t, .)) is tight in the space of probability measures on continuous functions and invoking the Krylov-Bogolyubov theorem. As we no longer have an a priori bound on our solution as in the two-barrier case, a key aspect of the proof is the derivation of a suitable Lp bound which is uniform in time.