Lipschitz Contractions, Unique Ergodicity and Asymptotics of Markov Semigroups
We are mainly concerned with the asymptotic behaviour of both discrete and continuous semigroups of Markov operators acting on the space of all continuous functions on a compact metric space . We establish a simple criterion under which such semigroups admit a unique invariant probability measure on that determines their limit behaviour on and on . The criterion involves the behaviour of the semigroups on Lipschitz continuous functions and on the relevant Lipschitz seminorms. Finally,...