On the large deviation principle for stationary weakly dependent random fields
type: Item
instance of: scholarly article
title: On the large deviation principle for stationary weakly dependent random fields
zbMATH Open document ID: 0756.60028
published in: The Annals of Probability
publication date: 1993-01-16T00:00:00Z
review text: Using a new criterion for the large deviation principle, the author proves the large deviation principle for the empirical field of a stationary \(\mathbb{Z}^ d\)-indexed random field. Different strong mixing assumptions are used to obtain the results for a compact or Polish space- valued random field. These assumptions allow to give a detailed description of the resulting rate function. Applications to empirical fields of Markov chains with a compact (or Polish) state space or to Gibbs fields with a countable state space and summable interaction potential are given.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60B12
zbMATH DE Number: 89799
zbMATH Keywords: large deviation principle
zbMATH Keywords: empirical field
zbMATH Keywords: random field
zbMATH Keywords: strong mixing
zbMATH Keywords: empirical fields of Markov chains
zbMATH Keywords: Gibbs fields
author: Włodek Bryc
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176989815
OpenAlex ID: W2009458774
DOI: 10.1214/AOP/1176989815
description: scientific article; zbMATH DE number 89799