Probability and Moment Inequalities for Additive Functionals of Geometrically Ergodic Markov Chains

Alain Durmus (), Eric Moulines (), Alexey Naumov () and Sergey Samsonov ()
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Alain Durmus: École polytechnique
Eric Moulines: École polytechnique
Alexey Naumov: HSE University
Sergey Samsonov: HSE University

Journal of Theoretical Probability, 2024, vol. 37, issue 3, 2184-2233

Abstract: 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 weighted total variation norm or in weighted Wasserstein distances. Our inequalities apply to unbounded functions and depend explicitly on constants appearing in the conditions that we consider.

Keywords: Concentration inequalities for Markov chains; Cumulant expansion; 60E15; 60J20; 65C40 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01315-7

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