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Markov operators acting on Polish spaces

Tomasz Szarek (1997)

Annales Polonici Mathematici

We prove a new sufficient condition for the asymptotic stability of Markov operators acting on measures. This criterion is applied to iterated function systems.

Markov operators on the space of vector measures; coloured fractals

Karol Baron, Andrzej Lasota (1998)

Annales Polonici Mathematici

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.

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