00974nas a2200133   4500000000100000008004100001260001200042100002100054700003200075245006200107856004700169490000700216520061700223       2024                            d  c03/20241 aRyszard Kukulski1 aHanna Wojewódka-Ściążko00aThe e-property of asymptotically stable Markov semigroups  uhttps://doi.org/10.1007/s00025-024-02134-20 v793 a<p>The relations between the e-property and the asymptotic stability of Markov semigroups are studied. In particular, it is shown that any stochastically continuous and asymptotically stable Markov-Feller semigroup with an invariant measure such that the interior of its support is non-empty satisfies the e-property. Moreover, it is proved that any Markov-Feller semigroup, which is stochastically continuous, and which possesses the eventual e-property, has the e-property as well. An example pointing out that such an implication does not have to hold without assuming stochastic continuity is provided.</p>