Invariant measure for a class of parabolic degenerate equations

In this paper we consider a stochastic flow in Rⁿ which leaves a closed convex set K invariant. By using a recent characterization of the invariance, involving the distance function, we study the corresponding transition semigroup P_t and its infinitesimal generator N. Due to the invariance property, N is a degenerate elliptic operator. We study existence of an invariant measure ν of P_t and the realization of N in L² (H, ν).