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

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

2011-07-21

arxiv.org/abs/1107.4353v2

Mathematics

Probability

24 pages and 2 figures. Complete revision of the previous version

Scientific paper

We derive 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.

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