The e-property of asymptotically stable Markov semigroups [1]
| Title | The e-property of asymptotically stable Markov semigroups |
| Publication Type | Journal Article |
| Year of Publication | Submitted |
| Authors | Kukulski R [2], Wojewódka-Ściążko H [3] |
| Journal | preprint |
| Keywords | asymptotic stability [4], Bounded-Lipschitz distance [5], e-property [6], equicontinuity [7], Markov semigroup [8], stochastic continuity [9] |
| Abstract | 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. |
| URL | https://arxiv.org/abs/2211.16424 [10] |
| DOI | 10.48550/ARXIV.2211.16424 [11] |