Markov approximation of chains of infinite order in the $\bar{d}$-metric

Creators: Gallo, Sandro; Lerasle, Matthieu; Takahashi, D.Y.

Others:: Instituto de Matemática da Universidade Federal do Rio de Janeiro (IM / UFRJ) ; Universidade Federal do Rio de Janeiro (UFRJ); Laboratoire Jean Alexandre Dieudonné (LJAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA); Ghazanfar's Lab ; Princeton University

Description

We derive explicit upper bounds for the d-distance between a chain of in nite order and its canonical k-steps Markov approximation. Our proof is entirely construc- tive and involves a \coupling from the past" argument. The new method covers non necessarily continuous probability kernels, and chains with null transition probabilities. These results imply in particular the Bernoulli property for these processes.

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Markov approximation of chains of infinite order in the $\bar{d}$-metric

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