On invariant measures associated to weakly coupled systems of Kolmogorov equations

In this paper, we deal with weakly coupled elliptic systems with unbounded coefficients. We prove the existence and characterize all the systems of invariant measures for the associated semigroup associated C_b(R^d;R^m). We also show some relevant properties of the extension of the semigroup to the L^p-spaces related to systems of invariant measures. Finally, we study the asymptotic behaviour of the semigroup as t tends to infinity.