The Kendall theorem and its application to the geometric ergodicity of Markov chains

Witold Bednorz. "The Kendall theorem and its application to the geometric ergodicity of Markov chains." Applicationes Mathematicae 40.2 (2013): 129-165. <http://eudml.org/doc/279924>.

@article{WitoldBednorz2013,
abstract = {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.},
author = {Witold Bednorz},
journal = {Applicationes Mathematicae},
keywords = {geometric ergodicity; renewal theory; Markov chain Monte Carlo},
language = {eng},
number = {2},
pages = {129-165},
title = {The Kendall theorem and its application to the geometric ergodicity of Markov chains},
url = {http://eudml.org/doc/279924},
volume = {40},
year = {2013},
}

TY - JOUR
AU - Witold Bednorz
TI - The Kendall theorem and its application to the geometric ergodicity of Markov chains
JO - Applicationes Mathematicae
PY - 2013
VL - 40
IS - 2
SP - 129
EP - 165
AB - 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.
LA - eng
KW - geometric ergodicity; renewal theory; Markov chain Monte Carlo
UR - http://eudml.org/doc/279924
ER -