We study the asymptotic behaviour of discrete time processes which are products of time dependent transformations defined on a complete metric space. Our sufficient condition is applied to products of Markov operators corresponding to stochastically perturbed dynamical systems and fractals.
Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
Bibliografia
[1] M. F. Barnsley, Fractals Everywhere, Academic Press, New York, 1988.
[2] M. F. Barnsley, S. G. Demko, J. H. Elton and J. S. Geronimo, Invariant measures arising from iterated function systems with place dependent probabilities, Ann. Inst. Henri Poincaré 24 (1988), 367-394.
[3] R. Fortet et B. Mourier, Convergence de la répartition empirique vers la répartition théorétique, Ann. Sci. École Norm. Sup. 70 (1953), 267-285.
[4] K. Horbacz, Dynamical systems with multiplicative perturbations: the strong convergence of measures, Ann. Polon. Math. 58 (1993), 85-93.
[5] J. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981), 713-747.
[6] A. Lasota, From fractals to stochastic differential equations, in: Chaos - The Interplay Between Stochastic and Deterministic Behaviour (Karpacz '95), Lecture Notes in Phys. 457, Springer, 1995, 235-255.
[7] A. Lasota and M. C. Mackey, Chaos, Fractals, and Noise-Stochastic Aspects of Dynamics, Springer, 1994.
[8] A. Lasota and M. C. Mackey, Stochastic perturbation of dynamical systems: the weak convergence of measures, J. Math. Anal. Appl. 138 (1989), 232-248.
[9] A. Lasota and J. Yorke, Lower bound technique for Markov operators and iterated function systems, Random Comput. Dynam. 2 (1994), 41-77.
[10] K. Łoskot and R. Rudnicki, Limit theorems for stochastically perturbed dynamical systems, J. Appl. Probab. 32 (1995), 459-469.
[11] K. Oczkowicz, Asymptotic stability of Markov operators corresponding to the dynamical systems with multiplicative perturbations, Ann. Math. Sil. 7 (1993), 99-108.
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Bibliografia
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