Open Access
November 1998 Large deviations of inverse processes with nonlinear scalings
N. G. Duffield, W. Whitt
Ann. Appl. Probab. 8(4): 995-1026 (November 1998). DOI: 10.1214/aoap/1028903372


We show, under regularity conditions, that a nonnegative nondecreasing real-valued stochastic process satisfies a large deviation principle (LDP) with nonlinear scaling if and only if its inverse process does. We also determine how the associated scaling and rate functions must be related. A key condition for the LDP equivalence is for the composition of two of the scaling functions to be regularly varying with nonnegative index. We apply the LDP equivalence to develop equivalent characterizations of the asymptotic decay rate in nonexponential asymptotics for queue-length tail probabilities. These alternative characterizations can be useful to estimate the asymptotic decay constant from systems measurements.


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N. G. Duffield. W. Whitt. "Large deviations of inverse processes with nonlinear scalings." Ann. Appl. Probab. 8 (4) 995 - 1026, November 1998.


Published: November 1998
First available in Project Euclid: 9 August 2002

zbMATH: 0939.60011
MathSciNet: MR1661311
Digital Object Identifier: 10.1214/aoap/1028903372

Primary: 60F10
Secondary: 60G18 , 60K25

Keywords: counting processes , inverse processes , large deviations , Queueing theory , regularly varying functions , renewal theory

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.8 • No. 4 • November 1998
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