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.
@article{1028903372,
author = {Duffield, N. G. and Whitt, W.},
title = {Large deviations of inverse processes with nonlinear
scalings},
journal = {Ann. Appl. Probab.},
volume = {8},
number = {1},
year = {1998},
pages = { 995-1026},
language = {en},
url = {http://dml.mathdoc.fr/item/1028903372}
}
Duffield, N. G.; Whitt, W. Large deviations of inverse processes with nonlinear
scalings. Ann. Appl. Probab., Tome 8 (1998) no. 1, pp. 995-1026. http://gdmltest.u-ga.fr/item/1028903372/