Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
217-234
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-05-19
Twórcy
autor
- Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
autor
- Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
Bibliografia
- [1] M. F. Barnsley, Fractals Everywhere, Academic Press, 1988.
- [2] M. F. Barnsley and S. Demko, Iterated function systems and the global construction of fractals, Proc. Roy. Soc. London Ser. A 399 (1985), 243-275.
- [3] J. Diestel and J. J. Uhl, Jr., Vector Measures, Amer. Math. Soc., 1977.
- [4] J. E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981), 713-747.
- [5] A. Lasota, From fractals to stochastic differential equations, in: P. Garbaczewski, M. Wolf and A. Weron (eds.), Chaos - The Interplay Between Stochastic and Deterministic Behaviour, Springer, 1995, 235-255.
- [6] A. Lasota and M. C. Mackey, Chaos, Fractals, and Noise. Stochastic Aspects of Dynamics, Springer, 1994.
- [7] A. Lasota and J. A. Yorke, Lower bound technique for Markov operators and iterated function systems, Random Comput. Dynam. 2 (1994), 41-77.
- [8] A. A. Markov, Extension of the law of large numbers for dependent variables, Izv. Fiz.-Mat. Obshch. Kazansk. Univ. (2) 15 (1906), 135-156 (in Russian).
- [9] E. Nummelin, General Irreducible Markov Chains and Non-negative Operators, Cambridge Univ. Press, 1984.
- [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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