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

Sandro Gallo (1) , Matthieu Lerasle (2) , D.Y. Takahashi (3)

1 IM / UFRJ - Instituto de Matemática da Universidade Federal do Rio de Janeiro
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 Ghazanfar's Lab

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.

Mots clés: Chains of in nite order; coupling from the past algorithms; canonical Markov approximation; d-distance

Domaines: Probabilités [math.PR]

Sandro Gallo, Matthieu Lerasle, D.Y. Takahashi. Markov approximation of chains of infinite order in the $\bar{d}$-metric. Markov Processes And Related Fields, 2013, 19 (1), pp.51--82. ⟨hal-00913858⟩