Geodesic
A criterion of asymptotic stability for Markov–Feller e-chains on Polish spaces
Dawid Czapla1
1 Institute of Mathematics University of Silesia Bankowa 14 40-007 Katowice, Poland
Annales Polonici Mathematici, Tome 105 (2012) no. 3, pp. 267-291 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ap105-3-5
Keywords: stettner bull polish acad sci math considered asymptotic stability markov feller chains provided sequence transition probabilities chain converges invariant probability measure weak sense converges uniformly respect initial state variable compact sets extend those results setting polish spaces relax original assumptions finally present class markov feller chains linear state space model which satisfy assumptions main theorem

Dawid Czapla 1

1 Institute of Mathematics University of Silesia Bankowa 14 40-007 Katowice, Poland 
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Dawid Czapla. A criterion of asymptotic stability for Markov–Feller e-chains on Polish spaces. Annales Polonici Mathematici, Tome 105 (2012) no. 3, pp. 267-291. doi: 10.4064/ap105-3-5

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