A criterion of asymptotic stability for Markov–Feller e-chains on Polish spaces

Volume 105 / 2012

Dawid Czapla Annales Polonici Mathematici 105 (2012), 267-291 MSC: Primary 60J05; Secondary 37A30. DOI: 10.4064/ap105-3-5

Abstract

Stettner [Bull. Polish Acad. Sci. Math. 42 (1994)] considered the asymptotic stability of Markov–Feller chains, provided the sequence of transition probabilities of the chain converges to an invariant probability measure in the weak sense and converges uniformly with respect to the initial state variable on compact sets. We extend those results to the setting of Polish spaces and relax the original assumptions. Finally, we present a class of Markov–Feller chains with a linear state space model which satisfy the assumptions of our main theorem.

Authors

  • Dawid CzaplaInstitute of Mathematics
    University of Silesia
    Bankowa 14
    40-007 Katowice, Poland
    e-mail

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