The stability of Markov operators on Polish spaces

Tomasz Szarek

Studia Mathematica (2000)

  • Volume: 143, Issue: 2, page 145-152
  • ISSN: 0039-3223

Abstract

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A sufficient condition for the asymptotic stability of Markov operators acting on measures defined on Polish spaces is presented.

How to cite

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Szarek, Tomasz. "The stability of Markov operators on Polish spaces." Studia Mathematica 143.2 (2000): 145-152. <http://eudml.org/doc/216813>.

@article{Szarek2000,
abstract = {A sufficient condition for the asymptotic stability of Markov operators acting on measures defined on Polish spaces is presented.},
author = {Szarek, Tomasz},
journal = {Studia Mathematica},
keywords = {asymptotic stability; Markov operators},
language = {eng},
number = {2},
pages = {145-152},
title = {The stability of Markov operators on Polish spaces},
url = {http://eudml.org/doc/216813},
volume = {143},
year = {2000},
}

TY - JOUR
AU - Szarek, Tomasz
TI - The stability of Markov operators on Polish spaces
JO - Studia Mathematica
PY - 2000
VL - 143
IS - 2
SP - 145
EP - 152
AB - A sufficient condition for the asymptotic stability of Markov operators acting on measures defined on Polish spaces is presented.
LA - eng
KW - asymptotic stability; Markov operators
UR - http://eudml.org/doc/216813
ER -

References

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  1. [1] 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. H. Poincaré 24 (1988), 367-394. Zbl0653.60057
  2. [2] P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968. Zbl0172.21201
  3. [3] R. M. Dudley, Probabilities and Metrics, Aarhus Universitet, 1976. 
  4. [4] S. Ethier and T. Kurtz, Markov Processes, Wiley, 1986. 
  5. [5] R. Fortet et B. Mourier, Convergence de la répartition empirique vers la répartition théorétique, Ann. Sci. École Norm. Sup. 70 (1953), 267-285. Zbl0053.09601
  6. [6] S. Karlin, Some random walks arising in learning models, Pacific J. Math. 3 (1953), 725-756. Zbl0051.10603
  7. [7] A. Lasota, From fractals to stochastic differential equations, in: Chaos-the Interplay between Stochastic and Deterministic Behaviour (Karpacz, 1995), Springer, 1995. 
  8. [8] 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
  9. [9] T. Szarek, Markov operators acting on Polish spaces, Ann. Polon. Math. 67 (1997), 247-257. Zbl0903.60052

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