Displaying similar documents to “On typical Markov operators acting on Borel measures.”

The uniqueness of invariant measures for Markov operators

Tomasz Szarek (2008)

Studia Mathematica

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It is shown that Markov operators with equicontinuous dual operators which overlap supports have at most one invariant measure. In this way we extend the well known result proved for Markov operators with the strong Feller property by R. Z. Khas'minski.

On a nonstandard approach to invariant measures for Markov operators

Andrzej Wiśnicki (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We show the existence of invariant measures for Markov-Feller operators defined on completely regular topological spaces which satisfy the classical positivity condition.

Invariant measures for iterated function systems

Tomasz Szarek (2000)

Annales Polonici Mathematici

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A new criterion for the existence of an invariant distribution for Markov operators is presented. Moreover, it is also shown that the unique invariant distribution of an iterated function system is singular with respect to the Hausdorff measure.

Markov operators on the space of vector measures; coloured fractals

Karol Baron, Andrzej Lasota (1998)

Annales Polonici Mathematici

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We consider the family 𝓜 of measures with values in a reflexive Banach space. In 𝓜 we introduce the notion of a Markov operator and using an extension of the Fortet-Mourier norm we show some criteria of the asymptotic stability. Asymptotically stable Markov operators can be used to construct coloured fractals.

On the classification of Markov chains via occupation measures

Onésimo Hernández-Lerma, Jean Lasserre (2000)

Applicationes Mathematicae

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We consider a Markov chain on a locally compact separable metric space X and with a unique invariant probability. We show that such a chain can be classified into two categories according to the type of convergence of the expected occupation measures. Several properties in each category are investigated.