On some results on the stability of Markov operators

Stanisław Wȩdrychowicz, Andrzej Wiśnicki

Published 2016-04-11Version 1

We formulate a criterion for the existence of an invariant measure for a Markov semigroup with the e-property defined on a metric space 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. We also clarify the status of the e-property by showing that four natural conditions are in fact equivalent.