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In this article, we establish Hoeffding's inequality for bounded Lipschitzfunctions of a class of not necessarily irreducible Markov models. The resultcomplements the existing literature on this topic where Hoeffding's inequalityfor bounded measurable functions of a class of irreducible Markov models hasbeen considered. Our approach is based on the assumption of uniform ergodicityof the underlying Markov model in $L^1$-Wasserstein space.

Hoeffding's inequality for non-irreducible Markov models