General Bernstein-Like Inequality for Additive Functionals of Markov Chains

Michał Lemańczyk ()
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Michał Lemańczyk: University of Warsaw

Journal of Theoretical Probability, 2021, vol. 34, issue 3, 1426-1454

Abstract: Abstract Using 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.

Keywords: General Markov chain; Concentration inequality; Bernstein inequality; 60E15; 60J05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-01006-z

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