English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

T. Szarek [Stud. Math. 189 (2008), {\S} 4] have discussed the relationshipbetween two important notions concerning Markov semigroups: the asymptoticstrong Feller property and the e-property, asserting that the former propertyimplies the latter one. In this very short note we rectify this issueexhibiting a simple example of a Markov-Feller semigroup enjoying theasymptotic strong Feller property, for which the e-property is not satisfied.(See also the comment on a connection between the asymptotic strong Fellerproperty and the e-property by T. Szarek, D. Worm [ETDS 32 (2012), {\S} 1]).Additionally we give a very simple example - in comparing with the one given byT. Szarek [Stud. Math. 189 (2008), {\S} 4] - showing that also the converseimplication does not hold.

The asymptotic strong Feller property does not imply the e-property for Markov-Feller semigroups