Time reversal and stationary Gibbs measures
type: Item
instance of: scholarly article
title: Time reversal and stationary Gibbs measures
zbMATH Open document ID: 0536.60096
DOI: 10.1016/0304-4149(84)90318-1
published in: Stochastic Processes and their Applications
publication date: 1984-01-01T00:00:00Z
review text: There exist many results saying that all time reversible stationary measures for an infinite particle system are Gibbsian with a potential determined by the transition mechanism. This paper gives an extension of this to the non reversible case with discrete time. The main result says that under some regularity conditions a stationary measure is Gibbs if and only if both the original and the time reversed transition kernels depend continuously on the initial values and then the potential is determined by these two kernels. The problem is somehow related to the problem of the global Markov property: One has to study the dependence of conditional distributions on the conditioning values when the available information is reduced. In continuous time similar but stronger results have been obtained in the author's paper ''Non reversible stationary measures for infinite interacting particle systems'', Z. Wahrscheinlichkeitstheor. Verw. Geb. 66, 407-424 (1984).
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 3852182
zbMATH Keywords: infinite particle systems
zbMATH Keywords: interaction
zbMATH Keywords: stationary measures for Markov chains
zbMATH Keywords: Gibbs measures
zbMATH Keywords: time reversal
zbMATH Keywords: global Markov property
MaRDI profile type: Publication
full work available at URL: 0304-4149(84)90318-1
OpenAlex ID: W2032393964
cites work: Synchronous and Asynchronous Reversible Markov Systems(1)
cites work: Q5576569
cites work: Prescribing a System of Random Variables by Conditional Distributions
cites work: Q3782526
cites work: Q3888306
cites work: Decay of correlations under Dobrushin's uniqueness condition and its applications
cites work: Q4137895
cites work: Q4130180
cites work: Potentials for almost Markovian random fields
cites work: Q4188565
author: H. R. Künsch
description: scientific article; zbMATH DE number 3852182