Markov operators acting on Polish spaces

Tomasz Szarek

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 3, page 247-257
  • ISSN: 0066-2216

Abstract

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

How to cite

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Tomasz Szarek. "Markov operators acting on Polish spaces." Annales Polonici Mathematici 67.3 (1997): 247-257. <http://eudml.org/doc/270502>.

@article{TomaszSzarek1997,
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.},
author = {Tomasz Szarek},
journal = {Annales Polonici Mathematici},
keywords = {Markov operators; iterated function systems; asymptotic stability; Markov operators on Polish spaces},
language = {eng},
number = {3},
pages = {247-257},
title = {Markov operators acting on Polish spaces},
url = {http://eudml.org/doc/270502},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Tomasz Szarek
TI - Markov operators acting on Polish spaces
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 3
SP - 247
EP - 257
AB - We prove a new sufficient condition for the asymptotic stability of Markov operators acting on measures. This criterion is applied to iterated function systems.
LA - eng
KW - Markov operators; iterated function systems; asymptotic stability; Markov operators on Polish spaces
UR - http://eudml.org/doc/270502
ER -

References

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  1. [1] M. F. Barnsley, Fractals Everywhere, Academic Press, New York, 1988. 
  2. [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. Zbl0613.28008
  3. [3] P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968. Zbl0172.21201
  4. [4] R. M. Dudley, Probabilities and Metrics, Aarhus Universitet, 1976. 
  5. [5] A. Lasota, From fractals to stochastic differential equations, to appear. Zbl0835.60058
  6. [6] A. Lasota and J. A. Yorke, Lower bound technique for Markov operators and iterated function systems, Random Comput. Dynam. 2 (1994), 41-77. Zbl0804.47033
  7. [7] K. Łoskot and R. Rudnicki, Limit theorems for stochastically perturbed dynamical systems, J. Appl. Probab. 32 (1995), 459-469. Zbl0829.60057
  8. [8] K. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York, 1967. Zbl0153.19101
  9. [9] T. Szarek, Iterated function systems depending on previous transformations, to appear. Zbl0888.47016

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