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On some results on the stability of Markov operators

Volume 241 / 2018

Stanisław Wędrychowicz, Andrzej Wiśnicki 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.

Authors

  • Stanisław WędrychowiczDepartment of Mathematics
    Rzeszów University of Technology
    Al. Powstańców Warszawy 12
    35-959 Rzeszów, Poland
    e-mail
  • Andrzej WiśnickiDepartment of Mathematics
    Rzeszów University of Technology
    Al. Powstańców Warszawy 12
    35-959 Rzeszów, Poland
    e-mail

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