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Markov operators acting on Polish spaces

100%
Szarek T.
Annales Polonici Mathematici
|
1997
|
tom 67
|
nr 3
247-257
EN
We prove a new sufficient condition for the asymptotic stability of Markov operators acting on measures. This criterion is applied to iterated function systems.
2
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Generic properties of learning systems

100%
Szarek T.
Annales Polonici Mathematici
|
2000
|
tom 73
|
nr 2
93-103
EN
It is shown that the set of learning systems having a singular stationary distribution is generic in the family of all systems satisfying the average contractivity condition.
3
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Infinite Graph-Directed Systems and Hausdorff Dimension

70%
Priyadarshi A.
Waves, Wavelets and Fractals
|
2017
|
tom 3
|
nr 1
84-95
EN
In this paper we study infinite graph-directed iterated function systems on compact metric spaces given by contractive ‘infinitesimal similitudes’. We derive formula for the Hausdorff dimension of the ‘invariant set’ for such a system in terms of the spectral radii of the naturally associated family of the ‘Perron- Frobenius operators’. The results in this paper generalizes the results obtained in [20], where finite graphdirected systems and infinite iterated function systems are considered
4
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Markov operators on the space of vector measures; coloured fractals

70%
Baron K., Lasota A.
Annales Polonici Mathematici
|
1998
|
tom 69
|
nr 3
217-234
EN
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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