A simple development of the Thouvenot relative isomorphism theory
type: Item
instance of: scholarly article
title: A simple development of the Thouvenot relative isomorphism theory
zbMATH Open document ID: 0551.28023
published in: The Annals of Probability
publication date: 1984-01-01T00:00:00Z
review text: Let \(X, Y, Z\) be processes with finite state space such that the pair processes \((X,Y)\), \((X,Z)\) are each stationary and ergodic. Thouvenot's relative isomorphism theorem says that these two pair processes are isomorphic (via stationary codes) if a) \(X\) and \(Y\) are independent; b) \(Y\) is a \(B\) process; c) \((X,Y)\) and \((X,Z)\) have the same entropy rate; and d) the process \(Z\) satisfies a condition called ``very weak Bernoulli relative to \(X\)''. The paper under review gives a simple proof of this result. Since the Ornstein isomorphism theorem is a special case of Thouvenot's result, one has as a consequence a simple proof of Ornstein's theorem as well.
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 94A24
zbMATH DE Number: 3877478
zbMATH Keywords: processes with finite state space
zbMATH Keywords: Thouvenot's relative isomorphism theorem
zbMATH Keywords: same entropy rate
zbMATH Keywords: very weak Bernoulli
zbMATH Keywords: Ornstein isomorphism theorem
author: John C. Kieffer
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176993383
OpenAlex ID: W1991561167
DOI: 10.1214/AOP/1176993383
description: scientific article; zbMATH DE number 3877478