Large deviations for empirical measures with degenerate limiting distribution
type: Item
instance of: scholarly article
title: Large deviations for empirical measures with degenerate limiting distribution
zbMATH Open document ID: 0793.60031
DOI: 10.1007/BF01199319
author: Terence Chan
publication date: 1994-08-11T00:00:00Z
review text: This paper studies the large deviations of the empirical measure associated with \(n\) independent random variables with a degenerate limiting distribution as \(n\to\infty\). A large deviations principle -- quite unlike the classical Sanov type results -- is established for such empirical measures in a general Polish space setting. This result is applied to the large deviations for the empirical process of a system of interacting particles, in which the diffusion coefficient vanishes as the number of particles tends to infinity. A second way in which the present example differs from previous work on similar weakly interacting systems is that there is a singularity in the mean-field type interaction.
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 568986
zbMATH Keywords: large deviations of the empirical measure
zbMATH Keywords: system of interacting particles
zbMATH Keywords: weakly interacting systems
zbMATH Keywords: mean-field type interaction
MaRDI profile type: Publication
cites work: Large deviations of the sample mean in general vector spaces
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full work available at URL: https://doi.org/10.1007/bf01199319
OpenAlex ID: W2020034306
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 568986