Functional approach of large deviations in general spaces
type: Item
instance of: scholarly article
title: Functional approach of large deviations in general spaces
zbMATH Open document ID: 1078.60019
author: Henri Comman
published in: Journal of Theoretical Probability
publication date: 2005-05-20T00:00:00Z
review text: Let \((\mu_{\alpha})\) be a net of Borel probability measures on a topological space \(X\), and \((t_{\alpha})\) a net in \(]0,{\infty}[\) converging to \(0\). For each \([-{\infty}, +{\infty}[\)-valued measurable function \(h\) on \(X\), we define \(\Lambda(h)=\log \lim (\int_X \exp{{h(x)}\over{t_\alpha}} \mu_{\alpha}(dx))^{t_\alpha}\) provided the limit exists in \([-\infty,+\infty]\). In order to prove a large deviation principle for \((\mu_{\alpha}^{t_\alpha})\), the so-called functional approach consists first to establish the existance of \(\Lambda(\cdot)\) on some class of continuous functions, and next to look for a sufficient condition, either of set-theoretic type, or on the functional \(\Lambda(\cdot)\). The author deals only with set-theoretic conditions. He presents a Prokhorov-type theorem with a weaker notion than exponential tightness, which improves known results.
reviewed by: Zdzisław Rychlik
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 2170059
zbMATH Keywords: Varadhan's theorem problem
MaRDI profile type: Publication
full work available at URL: s10959-004-2594-2
OpenAlex ID: W2032972041
cites work: Criteria for large deviations
cites work: Sequences of capacities, with connections to large-deviation theory
cites work: Q5613067
DOI: 10.1007/S10959-004-2594-2
description: scientific article; zbMATH DE number 2170059