IUMJ

Title: Invariant measures associated to degenerate elliptic operators

Authors: P. Cannarsa, G. Da Prato and H. Frankowska

Issue: Volume 59 (2010), Issue 1, 53-78

Abstract:

This paper is devoted to the study of the existence and uniqueness of the invariant measure associated to the transition semigroup of a diffusion process in a bounded open subset of $\mathbb{R}^n$. For this purpose, we investigate first the invariance of a bounded open domain with piecewise smooth boundary showing that such a property holds true under the same conditions that insure the invariance of the closure of the domain. A uniqueness result for the invariant measure is obtained in the class of all probability measures that are absolutely continuous with respect to Lebesgue's measure. A sufficient condition for the existence of such a measure is also provided.