no. 12
Functional analysis/Probability theory
Equicontinuous families of Markov operators in view of asymptotic stability
[Familles équicontinues d'opérateurs markoviens du point de vue de la stabilité asymptotique]

Présenté par : the Editorial Board

Hille, Sander Cornelis1 ; Szarek, Tomasz2 ; Ziemlańska, Maria Aleksandra1
1 Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands
2 Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
Comptes Rendus. Mathématique, Tome 355 (2017) no. 12, pp. 1247-1251.

Nous étudions la relation entre l'équicontinuite – la dite e-propriété – et la stabilité d'opérateurs de Markov. En particulier, nous montrons que tout opérateur markovien asymptotiquement stable, avec une mesure invariante telle que l'intérieur de son support est non vide, satisfait la e-propriété.

The relation between the equicontinuity – the so-called e-property – and the stability of Markov operators is studied. In particular, it is shown that any asymptotically stable Markov operator with an invariant measure such that the interior of its support is non-empty satisfies the e-property.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.10.019
Hille, Sander Cornelis 1 ; Szarek, Tomasz 2 ; Ziemlańska, Maria Aleksandra 1

1 Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands
2 Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland 
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Hille, Sander Cornelis; Szarek, Tomasz; Ziemlańska, Maria Aleksandra. Equicontinuous families of Markov operators in view of asymptotic stability. Comptes Rendus. Mathématique, Tome 355 (2017) no. 12, pp. 1247-1251. doi : 10.1016/j.crma.2017.10.019. http://www.numdam.org/articles/10.1016/j.crma.2017.10.019/

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Cité par Sources :

☆ The work of Maria Aleksandra Ziemlańska has been partially supported by a Huygens Fellowship of Leiden University. The work of Tomasz Szarek has been supported by the National Science Centre of Poland, grant number 2016/21/B/ST1/00033.