Subgaussian concentration inequalities for geometrically ergodic Markov chains

Abstract : We prove that an irreducible aperiodic Markov chain is geometrically ergodic if and only if any separately bounded functional of the stationary chain satisfies an appropriate subgaussian deviation inequality from its mean.
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Jérôme Dedecker, Sébastien Gouëzel. Subgaussian concentration inequalities for geometrically ergodic Markov chains. Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2015, 20 (article 64), ⟨10.1214/ECP.v20-3966⟩. ⟨hal-01091212v2⟩

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