Weak Pinsker property and Markov processes
type: Item
instance of: scholarly article
title: Weak Pinsker property and Markov processes
zbMATH Open document ID: 0617.28018
author: Alain Rosenthal
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1986-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77284
review text: Pinsker's conjecture was that every ergodic dynamical system can be written as the direct product of a K-system and a system of O-entropy. This was proved to be false by D. Ornstein. Then, J.-P. Thouvenot introduced a weaker notion, called weak Pinsker property: A system has this property if it can be written as the direct product of a Bernoulli and a system of arbitrary small entropy. It is the purpose of the paper to show that all the ergodic \({\mathbb{Z}}^ 2\)-Markov processes have this weak Pinsker property.
Mathematics Subject Classification ID: 28D15
Mathematics Subject Classification ID: 60J99
zbMATH DE Number: 4000284
zbMATH Keywords: weak Pinsker property
zbMATH Keywords: Bernoulli
zbMATH Keywords: ergodic \({bbfZ}^ 2\)-Markov processes
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4000284