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 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.

Exposition changed, the results for the geometrically ergodic case stated separately, some examples and a comparison with other recent inequalities added

References in corpus (3)

• Concentration around the mean for maxima of empirical processes
• Renewal theory and computable convergence rates for geometrically ergodic Markov chains
• Concentration inequalities for dependent Random variables via the martingale method

Cited by in corpus (2)

• Non parametric finite translation mixtures with dependent regime
• Some remarks on MCMC estimation of spectra of integral operators