Markov Approximation of Chains of Infinite Order in the $\bar{d}$-metric
S. Gallo, M. Lerasle, D.Y. Takahashi
2013, v.19, Issue 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
COMMENTS
Please log in or register to leave a comment
There are no comments yet