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arXiv · 2105.09536

On the $\alpha$-lazy version of Markov chains in estimation and testing problems

Sela Fried·Geoffrey Wolfer
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Abstract

Given access to a single long trajectory generated by an unknown irreducible Markov chain $M$, we simulate an $\alpha$-lazy version of $M$ which is ergodic. This enables us to generalize recent results on estimation and identity testing that were stated for ergodic Markov chains in a way that allows fully empirical inference. In particular, our approach shows that the pseudo spectral gap introduced by Paulin [2015] and defined for ergodic Markov chains may be given a meaning already in the case of irreducible but possibly periodic Markov chains.

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Sela Fried, Geoffrey Wolfer. 2021-05-20. On the $\alpha$-lazy version of Markov chains in estimation and testing problems. https://arxiv.org/abs/2105.09536

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