| Issue |
ESAIM: PS
Volume 19, 2015
|
|
|---|---|---|
| Page(s) | 440 - 481 | |
| DOI | https://doi.org/10.1051/ps/2014032 | |
| Published online | 11 November 2015 | |
Exponential concentration inequalities for additive functionals of Markov chains∗,∗∗
University of Warsaw, Banacha 2, 02-097
Warszawa,
Poland
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Received: 22 August 2013
Revised: 6 June 2014
Abstract
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.
Mathematics Subject Classification: 60E15 / 60J20 / 60K05 / 65C05
Key words: Markov chains / exponential inequalities / drift criteria
Research partially supported by MNiSW Grant N N201 608740 and the Foundation for Polish Science.
Research partially supported by MNiSW Grant N N201 608740.
© EDP Sciences, SMAI, 2015
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