The large deviations of estimating rate functions

The large deviations of estimating rate functions

Ken Duffy and Anthony P. Metcalfe

Source: J. Appl. Probab. Volume 42, Number 1 (2005), 267-274.

Abstract

Given a sequence of bounded random variables that satisfies a well-known mixing condition, it is shown that empirical estimates of the rate function for the partial sums process satisfy the large deviation principle in the space of convex functions equipped with the Attouch-Wets topology. As an application, a large deviation principle for estimating the exponent in the tail of the queue length distribution at a single-server queue with infinite waiting space is proved.

First Page: Show

Primary Subjects: 60F10

Secondary Subjects: 60K25

Keywords: Large deviation estimate; queue length tail estimate

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jap/1110381386
Digital Object Identifier: doi:10.1239/jap/1110381386
Mathematical Reviews number (MathSciNet): MR2144909
Zentralblatt MATH identifier: 1077.60028

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