The e-property of asymptotically stable Markov semigroups

TytułThe e-property of asymptotically stable Markov semigroups
Publication TypeJournal Article
Rok publikacjiSubmitted
AutorzyKukulski R, Wojewódka-Ściążko H
Słowa kluczoweasymptotic stability, Bounded-Lipschitz distance, e-property, equicontinuity, Markov semigroup, stochastic continuity

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.


Historia zmian

Data aktualizacji: 20/10/2023 - 15:21; autor zmian: Hanna Wojewódka Ściążko (