Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Ergodic Markov chains are not determined by any p-marginals

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Résumé: We prove that if $X=(X_n)_{n\in Z}$ is a finite valued ergodic Markov Chain, then for any natural number $p$, there exist ergodic non-Markovian processes $Y=(Y_n)_{n\in Z}$ with positive entropy, such that for all integers $n_1,...,n_p$, the joint distribution of $Y_{n_1},...,Y_{n_p}$ is identical to the joint distribution of $X_{n_1},...,X_{n_p}$.

Mots Clés: Ergodic Markov Chain ; finite dimensional marginals ; dynamical system ; entropy

Date: 2000-09-18

Prépublication numéro: PMA-612