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On some results on the stability of Markov operators (1604.02968v3)
Published 11 Apr 2016 in math.PR and math.FA
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.
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