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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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