Exponential concentration inequalities for additive functionals of Markov chains

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 have all the constants accessible whenever the usual drift condition holds, which is crucial for practical applications e.g. in MCMC algorithms. AMS 2000 subject classifications : Primary 60E15, 60J20, secondary 60K05, 65C05