The e-property of asymptotically stable Markov semigroups
| Author | Kukulski R.; Wojewódka-Ściążko H. |
|---|---|
| Title | The e-property of asymptotically stable Markov semigroups |
| Journal | Results in Mathematics |
| Year | 2024 |
| Status | Published |
| Volume | 79 |
| Issue | 112 |
| DOI | 10.1007/s00025-024-02134-2 |
| URL | https://doi.org/10.1007/s00025-024-02134-2 |
| Abstract | <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> |