Compactness in the theory of large deviations
type: Item
instance of: scholarly article
title: Compactness in the theory of large deviations
zbMATH Open document ID: 0824.60019
DOI: 10.1016/0304-4149(95)00007-T
author: George L. O'Brien
author: Wim Vervaat
published in: Stochastic Processes and their Applications
publication date: 1995-05-23T00:00:00Z
review text: Large deviation principles are expressed as the vague or narrow convergence of sequences of the set functions called capacities. As an application, a short proof of Gärtner-Ellis criterion for the large deviation principle is given. The capacity methods introduced in the paper are also used in forthcoming papers [\textit{G. L. O'Brien}, Sequences of capacities, with connections to large-deviation theory, J. Theor. Probab. (to appear) and \textit{W. Bryc} and \textit{A. Dembo}, Large deviations and strong mixing, Ann. Inst. Henri Poincaré, Probab. Stat. (to appear)].
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 757537
zbMATH Keywords: capacities
zbMATH Keywords: large deviation principles
zbMATH Keywords: Gärtner-Ellis criterion
reviewed by: Włodek Bryc
MaRDI profile type: Publication
cites work: Q5560061
cites work: Q3212057
cites work: Upper bounds for large deviations of dependent random vectors
cites work: Q3134548
cites work: A function space large deviation principle for certain stochastic integrals
cites work: Identifying a large deviation rate function
cites work: Q4085497
cites work: Large deviations for a general class of random vectors
cites work: Q3681702
cites work: On Large Deviations from the Invariant Measure
cites work: Large deviations for processes with independent increments
cites work: Q3212058
cites work: Q4695445
cites work: The method of stochastic exponentials for large deviations
cites work: Q5638112
cites work: Asymptotic probabilities and differential equations
description: scientific article; zbMATH DE number 757537