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General Bernstein-Like Inequality for Additive Functionals of Markov Chains

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  • Michał Lemańczyk

    (University of Warsaw)

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.

Suggested Citation

  • Michał Lemańczyk, 2021. "General Bernstein-Like Inequality for Additive Functionals of Markov Chains," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1426-1454, September.
  • Handle: RePEc:spr:jotpro:v:34:y:2021:i:3:d:10.1007_s10959-020-01006-z
    DOI: 10.1007/s10959-020-01006-z
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