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ArticleOriginal scientific text

Title

Stability of Markov processes nonhomogeneous in time

Authors 1

Affiliations

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

Abstract

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.

Keywords

ENG
asymptotic stability, Markov operator, dynamical system

Bibliography

  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.
Annales Polonici Mathematici
1999/71/1
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Pages:
47-59
Main language of publication
English
Received
1998-04-08
Accepted
1998-07-13
Published
1999
Exact and natural sciences