Geodesic
Exponential concentration inequalities for additive functionals of Markov chains
Adamczak, Radosław1 ; Bednorz, Witold1
1 University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
ESAIM: Probability and Statistics, Tome 19 (2015), pp. 440-481 Cet article a éte moissonné depuis la source Numdam

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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.

Reçu le :
DOI : 10.1051/ps/2014032
Classification : 60E15, 60J20, 60K05, 65C05
Keywords: Markov chains, exponential inequalities, drift criteria

Adamczak, Radosław 1 ; Bednorz, Witold 1

1 University of Warsaw, Banacha 2, 02-097 Warszawa, Poland 
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     title = {Exponential concentration inequalities for additive functionals of {Markov} chains},
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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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