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Article Dans Une Revue Journal of Statistical Physics Année : 2010

Perfect simulation of a coupling achieving the $\bar{d}$-distance between ordered pairs of binary chains of infinite order

Résumé

We explicitly construct a stationary coupling attaining Ornstein's $\bar{d}$-distance between ordered pairs of binary chains of infinite order. Our main tool is a representation of the transition probabilities of the coupled bivariate chain of infinite order as a countable mixture of Markov transition probabilities of increasing order. Under suitable conditions on the loss of memory of the chains, this representation implies that the coupled chain can be represented as a concatenation of iid sequences of bivariate finite random strings of symbols. The perfect simulation algorithm is based on the fact that we can identify the first regeneration point to the left of the origin almost surely.
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Dates et versions

hal-00770585 , version 1 (07-01-2013)

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Antonio Galves, Nancy L. Garcia, Clémentine Prieur. Perfect simulation of a coupling achieving the $\bar{d}$-distance between ordered pairs of binary chains of infinite order. Journal of Statistical Physics, 2010, 141 (4), pp.669-682. ⟨10.1007/s10955-010-0071-0⟩. ⟨hal-00770585⟩
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