An ergodic Markov chain is not determined by any p-marginals |
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| Authors: | D. Hamdan |
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| Affiliation: | Laboratoire de Probabilités et Modèles Aléatoires, CNRS-UMR 7599, Université Paris VI et Université Paris VII, Tour 56 (3e étage), Boîte courrier 188, 4 Place Jussieu, F-75752, Paris Cedex 05, France |
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| Abstract: | We prove that if X = (Xn)nεZ is a finite state space ergodic Markov chain, then for any natural number p, there exist ergodic non-Markovian processes Y = (Yn)nεZ with positive entropy, such that for all integers n1, …, np, the joint distribution of Yn1, …, Ynp is identical to the joint distribution of Xn1, …, Xnp. |
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