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Using the renewal approach we prove exponential inequalities for additive functionals and empirical processes of ergodic Markov chains, thus obtaining counterparts of inequalities for sums of independent random variables. The inequalities do not require functions of the chain to be bounded and moreover all the involved constants are given by explicit formulas whenever the usual drift condition holds, which may be of interest in practical applications e.g. to MCMC algorithms.
Adamczak, Radosław 1 ; Bednorz, Witold 1
@article{PS_2015__19__440_0,
author = {Adamczak, Rados{\l}aw and Bednorz, Witold},
title = {Exponential concentration inequalities for additive functionals of {Markov} chains},
journal = {ESAIM: Probability and Statistics},
pages = {440--481},
publisher = {EDP-Sciences},
volume = {19},
year = {2015},
doi = {10.1051/ps/2014032},
zbl = {1364.60028},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2014032/}
}
TY - JOUR AU - Adamczak, Radosław AU - Bednorz, Witold TI - Exponential concentration inequalities for additive functionals of Markov chains JO - ESAIM: Probability and Statistics PY - 2015 SP - 440 EP - 481 VL - 19 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps/2014032/ DO - 10.1051/ps/2014032 LA - en ID - PS_2015__19__440_0 ER -
%0 Journal Article %A Adamczak, Radosław %A Bednorz, Witold %T Exponential concentration inequalities for additive functionals of Markov chains %J ESAIM: Probability and Statistics %D 2015 %P 440-481 %V 19 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps/2014032/ %R 10.1051/ps/2014032 %G en %F PS_2015__19__440_0
Adamczak, Radosław; Bednorz, Witold. Exponential concentration inequalities for additive functionals of Markov chains. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 440-481. doi: 10.1051/ps/2014032
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