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The Large Deviations of Estimating Rate Functions

Part of: Special processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Ken Duffy  and
Anthony P. Metcalfe
Ken Duffy*
Affiliation:
National University of Ireland, Maynooth
Anthony P. Metcalfe*
Affiliation:
Trinity College Dublin
*
∗Postal address: Hamilton Institute, National University of Ireland, Maynooth, County Kildare, Ireland. Email address: ken.duffy@nuim.ie
∗∗Postal address: Department of Pure and Applied Mathematics, Trinity College Dublin, Ireland.
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Abstract

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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.

Keywords

Large deviation estimatequeue length tail estimate

MSC classification

Secondary: 60F10: Large deviations 60K25: Queueing theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 42 , Issue 1 , March 2005 , pp. 267 - 274
Copyright
© Applied Probability Trust 2005 

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