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On the existence of an invariant measure for Markov-Feller operators |
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| Authors: | Jó zef Myjak,Tomasz Szarek |
| Affiliation: | a Dipartimento di Matematica Pura ed Applicata, Università di L'Aquila, Via Vetoio, 67100 L'Aquila, Italy b WMS AGH, al. Mickiewicza 30, 30-059 Kraków, Poland c Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland d Department of Mathematics Technical University of Rzeszów, W. Pola 6, 35-959 Rzeszów, Poland |
| Abstract: | Let X be a Polish space and P a Markov operator acting on the space of Borel measures on X. We will prove the existence of an invariant measure with respect to P, provided that P satisfies some condition of a Prokhorov type and that the family of functions  is equi-continuous with respect to the Prokhorov distance at some point of the space X. Moreover, we will construct a counterexample which show that the above equi-continuity condition cannot be dropped. |
| Keywords: | Markov operators Invariant measure Dynamical systems Stability |
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