Sur les processus quasi-Markoviens et certains de leurs facteurs

Thierry de la Rue¹

¹ Laboratoire de Mathématiques Raphaël Salem UMR 6085 CNRS – Université de Rouen Avenue de l'Université, B.P. 12 F-76801 Saint-Étienne-du-Rouvray Cedex, France

Colloquium Mathematicum, Tome 103 (2005) no. 2, pp. 215-230.

Résumé

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.

Détail

DOI : 10.4064/cm103-2-7

Mots-clés : study class stationary finite state processes called quasi markovian including particular processes whose law gibbs measure defined bowen factor integrable coding time quasi markovian process maximal entropy factor splits off which means admits bernoulli shift independent complement maximal entropy splitting finite extension factor which generalizes theorem rahe particular result applies factor hyperbolic automorphism torus generated partition which regular enough