Sample path large deviations in finer topologies

In this paper we present sufficient conditions for sample path large deviation principles to be extended to finer topologies. We consider extensions of the uniform topology by Orlicz functional and we consider Lipschitz spaces: the former are concerned with cumulative path behavior while the latter...

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Bibliographic Details
Published inStochastics and stochastics reports Vol. 67; no. 3-4; pp. 231 - 254
Main Authors Eichelsbacher, Peter, O'connell, Neil
Format Journal Article
LanguageEnglish
Published Abingdon Gordon and Breach Science Publishers 01.09.1999
Taylor & Francis
Subjects
1991 Mathematics Subject Classifications
Exact sciences and technology
Functional analysis
Large deviations
Limit theorems
Lipschitz space
Mathematical analysis
Mathematics
Orlicz-space
partial sums
Primary: 60F10, 60G17, 46E30
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Stochastic processes
Large deviation principle
Chernoff inequality
Partial sum
Lipschitz space
Functional analysis
Orlicz space
Large deviation
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Summary:In this paper we present sufficient conditions for sample path large deviation principles to be extended to finer topologies. We consider extensions of the uniform topology by Orlicz functional and we consider Lipschitz spaces: the former are concerned with cumulative path behavior while the latter are more sensitive to extremes in local variation. We also consider sample paths indexed by the half line, where the usual projective limit topologies are not strong enough for many applications. We introduce and apply a new technique extending large deviation principles to finer topologies. We show how to apply the results to obtain large deviations for weighted statistics, to improve Schilder's theorem as well as to obtain large deviations in queueing theory
ISSN:1045-1129
DOI:10.1080/17442509908834212