Probability and moment inequalities for additive functionals of geometrically ergodic Markov chains

Alain Durmus; Eric Moulines; Alexey Naumov; Sergey Samsonov

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arXiv · 2109.00331

Probability and moment inequalities for additive functionals of geometrically ergodic Markov chains

Alain Durmus·Eric Moulines·Alexey Naumov·Sergey Samsonov

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Abstract

In this paper, we establish moment and Bernstein-type inequalities for additive functionals of geometrically ergodic Markov chains. These inequalities extend the corresponding inequalities for independent random variables. Our conditions cover Markov chains converging geometrically to the stationary distribution either in $V$-norms or in weighted Wasserstein distances. Our inequalities apply to unbounded functions and depend explicitly on constants appearing in the conditions that we consider.

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Alain Durmus, Eric Moulines, Alexey Naumov, Sergey Samsonov. 2021-09-01. Probability and moment inequalities for additive functionals of geometrically ergodic Markov chains. https://arxiv.org/abs/2109.00331

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