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.
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.
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Sander Cornelis Hille 1; Tomasz Szarek 2; Maria Aleksandra Ziemlańska 1
@article{CRMATH_2017__355_12_1247_0, author = {Sander Cornelis Hille and Tomasz Szarek and Maria Aleksandra Ziemla\'nska}, title = {Equicontinuous families of {Markov} operators in view of asymptotic stability}, journal = {Comptes Rendus. Math\'ematique}, pages = {1247--1251}, publisher = {Elsevier}, volume = {355}, number = {12}, year = {2017}, doi = {10.1016/j.crma.2017.10.019}, language = {en}, }
TY - JOUR AU - Sander Cornelis Hille AU - Tomasz Szarek AU - Maria Aleksandra Ziemlańska TI - Equicontinuous families of Markov operators in view of asymptotic stability JO - Comptes Rendus. Mathématique PY - 2017 SP - 1247 EP - 1251 VL - 355 IS - 12 PB - Elsevier DO - 10.1016/j.crma.2017.10.019 LA - en ID - CRMATH_2017__355_12_1247_0 ER -
%0 Journal Article %A Sander Cornelis Hille %A Tomasz Szarek %A Maria Aleksandra Ziemlańska %T Equicontinuous families of Markov operators in view of asymptotic stability %J Comptes Rendus. Mathématique %D 2017 %P 1247-1251 %V 355 %N 12 %I Elsevier %R 10.1016/j.crma.2017.10.019 %G en %F CRMATH_2017__355_12_1247_0
Sander Cornelis Hille; Tomasz Szarek; Maria Aleksandra Ziemlańska. Equicontinuous families of Markov operators in view of asymptotic stability. Comptes Rendus. Mathématique, Volume 355 (2017) no. 12, pp. 1247-1251. doi : 10.1016/j.crma.2017.10.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.10.019/
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☆ 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.
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