We study a class of stationary finite state processes, called quasi-Markovian, including in particular the processes whose law is a Gibbs measure as defined by Bowen. We show that, if a factor with integrable coding time of a quasi-Markovian process is maximal in entropy, then this factor splits off, which means that it admits a Bernoulli shift as an independent complement. If it is not maximal in entropy, then we can find a splitting finite extension of this factor, which generalizes a theorem of Rahe. In particular, this result applies to a factor of a hyperbolic automorphism of the torus generated by a partition which is regular enough.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-2-7,
author = {Thierry de la Rue},
title = {Sur les processus quasi-Markoviens et certains de leurs facteurs},
journal = {Colloquium Mathematicae},
volume = {103},
year = {2005},
pages = {215-230},
zbl = {1098.37005},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-2-7}
}
Thierry de la Rue. Sur les processus quasi-Markoviens et certains de leurs facteurs. Colloquium Mathematicae, Tome 103 (2005) pp. 215-230. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-2-7/