Abstract
AbstractUsing the renewal approach, we prove Bernstein-like inequalities for additive functionals of geometrically ergodic Markov chains, thus obtaining counterparts of inequalities for sums of independent random variables. The coefficient in the sub-Gaussian part of our estimate is the asymptotic variance of the additive functional, i.e., the variance of the limiting Gaussian variable in the central limit theorem for Markov chains. This refines earlier results by Adamczak and Bednorz, obtained under the additional assumption of strong aperiodicity of the chain.
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
1 articles.
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