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Subgaussian concentration inequalities for geometrically ergodic Markov chains. (English) Zbl 1329.60251

Summary: 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.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60E15 Inequalities; stochastic orderings