Markov operators on the space of vector measures; coloured fractals

• Autorzy: Karol Baron , Andrzej Lasota
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

vector measures; Fortet-Mourier norm; Markov operators; asymptotic stability; iterated function systems

Kategorie tematyczne

• 60J05: Discrete-time Markov processes on general state spaces
• 39B12: Iteration theory, iterative and composite equations
• 28B05: Vector-valued set functions, measures and integrals
• 46G10: Vector-valued measures and integration

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1998
• Tom: 69
• Numer: 3
• Strony: 217-234

Daty

wydano

1998

otrzymano

1997-05-19

Twórcy

autor

Karol Baron

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

autor

Andrzej Lasota

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

Bibliografia

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• [6] A. Lasota and M. C. Mackey, Chaos, Fractals, and Noise. Stochastic Aspects of Dynamics, Springer, 1994.
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• [10] K. R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, 1967.
• [11] S. T. Rachev, Probability Metrics and the Stability of Stochastic Models, Wiley, 1991.