Geodesic
The Kendall theorem and its application to the geometric ergodicity of Markov chains
Witold Bednorz1
1 Institute of Mathematics Warsaw University 02-097 Warszawa, Poland
Applicationes Mathematicae, Tome 40 (2013) no. 2, pp. 129-165 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We give an improved quantitative version of the Kendall theorem. The Kendall theorem states that under mild conditions imposed on a probability distribution on the positive integers (i.e. a probability sequence) one can prove convergence of its renewal sequence. Due to the well-known property (the first entrance last exit decomposition) such results are of interest in the stability theory of time-homogeneous Markov chains. In particular this approach may be used to measure rates of convergence of geometrically ergodic Markov chains and consequently implies estimates on convergence of MCMC estimators.
DOI : 10.4064/am40-2-1
Keywords: improved quantitative version kendall theorem kendall theorem states under mild conditions imposed probability distribution positive integers probability sequence prove convergence its renewal sequence due well known property first entrance exit decomposition results interest stability theory time homogeneous markov chains particular approach may measure rates convergence geometrically ergodic markov chains consequently implies estimates convergence mcmc estimators

Witold Bednorz 1

1 Institute of Mathematics Warsaw University 02-097 Warszawa, Poland 
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Witold Bednorz. The Kendall theorem and its application to the geometric ergodicity of Markov chains. Applicationes Mathematicae, Tome 40 (2013) no. 2, pp. 129-165. doi: 10.4064/am40-2-1

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