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1998 | 69 | 3 | 217-234
Tytuł artykułu

Markov operators on the space of vector measures; coloured fractals

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Abstrakty
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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.
Twórcy
autor
  • Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
  • 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
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bwmeta1.element.bwnjournal-article-apmv69z3p217bwm
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