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arXiv · 1908.06240

Markov chains with exponential return times are finitary

Omer Angel·Yinon Spinka
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Abstract

Consider an ergodic Markov chain on a countable state space for which the return times have exponential tails. We show that the stationary version of any such chain is a finitary factor of an i.i.d. process. A key step is to show that any stationary renewal process whose jump distribution has exponential tails and is not supported on a proper subgroup of $\mathbb{Z}$ is a finitary factor of an i.i.d. process.

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Omer Angel, Yinon Spinka. 2019-08-17. Markov chains with exponential return times are finitary. https://doi.org/10.1017/etds.2020.100

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