Exponential tightness can fail in the strong topology
type: Item
instance of: scholarly article
title: Exponential tightness can fail in the strong topology
zbMATH Open document ID: 0938.60026
DOI: 10.1016/S0167-7152(98)00127-8
author: Peter Eichelsbacher
author: Malte Grunwald
published in: Statistics \& Probability Letters
publication date: 2000-06-21T00:00:00Z
review text: The authors point out that a large deviations principle does not imply the exponential tightness in general. In Theorem 1.1 they prove for the classical Sanov result that the exponential tightness holds in the strong topology if and only if the underlying measure is purely atomic. In some remarks exercises or results by several authors are cited [see \textit{P. Gänssler}, Z. Wahrscheinlichkeitstheorie Verw. Geb. 17, 124-146 (1971; Zbl 0195.33902); \textit{J. Lynch} and \textit{J. Sethuraman}, Ann. Probab. 15, 610-627 (1987; Zbl 0624.60045); \textit{A. Dembo} and \textit{O. Zeitouni}, ``Large deviations techniques and applications'' (1993; Zbl 0793.60030); \textit{A. de Acosta}, in: Studies in applied probability. Essays in honour of Lajos Takács, 41-47 (1994; Zbl 0810.60022); \textit{D. W. Stroock}, ``Probability theory: an analytic view'' (Cambridge, 1993)].
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 1348355
zbMATH Keywords: exponential tightness
zbMATH Keywords: strong topology
zbMATH Keywords: large deviations
reviewed by: Ludwig Paditz
MaRDI profile type: Publication
cites work: On large deviations of empirical measures in the τ-topology
cites work: Q3134548
cites work: Compactness and sequential compactness in spaces of measures
cites work: Large deviations for processes with independent increments
cites work: Q4284032
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description: scientific article; zbMATH DE number 1348355