Copules gaussiennes dans les chaînes triplet partiellement de Markov

Hidden Markov chains, which are widely used in different data restoration problems, have recently been generalised to pairwise partially Markov chains, in which the hidden chain is no longer necessarily Markovian and the distribution of the observed chain, conditional on the hidden one, is of any form. First, we show the applicability of the models in the Gaussian case, with a particular attention to long range correlation noises. Second, we show that the use of copulas allows one to take into account any other form of marginal distributions of the observed chain, conditionally to the hidden one. We end by extending the latter model to a triplet partially Markov chain case. To cite this article: W. Pieczynski, C. R. Acad. Sci. Paris, Ser. I 341 (2005).