On some results on the stability of Markov operators
Volume 241 / 2018
Studia Mathematica 241 (2018), 41-55
MSC: Primary 60J25; Secondary 37A30, 47D07, 60J05, 60J35.
DOI: 10.4064/sm8584-3-2017
Published online: 14 September 2017
Abstract
We formulate a criterion for the existence of an invariant measure for a Feller semigroup defined on a metric space with the e-property for bounded continuous functions and use it to prove the asymptotic stability of a semigroup satisfying a lower bound condition. Our results complement those of A. Lasota and J. A. Yorke in proper metric spaces and of T. Szarek in Polish spaces.
