Download PDF - Markov operators acting on Polish spacesAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Markov operators acting on Polish spaces

Authors 1

Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Staromiejska 8/6, 40-013 Katowice, Poland

Abstract

We prove a new sufficient condition for the asymptotic stability of Markov operators acting on measures. This criterion is applied to iterated function systems.

Keywords

ENG
Markov operators, iterated function systems

Bibliography

  1. M. F. Barnsley, Fractals Everywhere, Academic Press, New York, 1988.
  2. M. F. Barnsley, V. Ervin, D. Hardin and J. Lancaster, Solution of an inverse problem for fractals and other sets, Proc. Nat. Acad. Sci. U.S.A. 83 (1986), 1975-1977.
  3. P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968.
  4. R. M. Dudley, Probabilities and Metrics, Aarhus Universitet, 1976.
  5. A. Lasota, From fractals to stochastic differential equations, to appear.
  6. A. Lasota and J. A. Yorke, Lower bound technique for Markov operators and iterated function systems, Random Comput. Dynam. 2 (1994), 41-77.
  7. K. Łoskot and R. Rudnicki, Limit theorems for stochastically perturbed dynamical systems, J. Appl. Probab. 32 (1995), 459-469.
  8. K. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York, 1967.
  9. T. Szarek, Iterated function systems depending on previous transformations, to appear.
Annales Polonici Mathematici
1997/67/3
Export to PBN, Opens in new tab
Pages:
247-257
Main language of publication
English
Received
1996-03-11
Accepted
1996-11-20
Published
1997
Exact and natural sciences