On some results on the stability of Markov operators

Abstract

We formulate a criterion for the existence of an invariant measure for a Feller semigroup defined on a metric space with the e-property for bounded continuous functions and use it to prove the asymptotic stability of a semigroup satisfying a lower bound condition. Our results complement those of A. Lasota and J. A. Yorke in proper metric spaces and of T. Szarek in Polish spaces.

arXiv comment14 pages, revised version, to appear in Studia Mathematica

Cited by in corpus (1)

• The e-property of asymptotically stable Markov semigroups