Probability and moment inequalities for additive functionals of geometrically ergodic Markov chains
Probability
2023-06-16 v2
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 -norms or in weighted Wasserstein distances. Our inequalities apply to unbounded functions and depend explicitly on constants appearing in the conditions that we consider.
Cite
@article{arxiv.2109.00331,
title = {Probability and moment inequalities for additive functionals of geometrically ergodic Markov chains},
author = {Alain Durmus and Eric Moulines and Alexey Naumov and Sergey Samsonov},
journal= {arXiv preprint arXiv:2109.00331},
year = {2023}
}