Markov Approximation of Chains of Infinite Order in the $\bar{d}$-metric

#### S. Gallo, M. Lerasle, D.Y. Takahashi

2013, v.19, №1, 51-82

ABSTRACT

We obtain explicit upper bounds for the $\bar{d}$-distance between a chain of infinite order and its canonical $k$-steps Markov approximation. Our proof is entirely constructive 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.

Keywords: chains of infinite order,coupling from the past algorithms,canonical Markov approximation,$\bar{d}$-distance

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