We apply an extended contraction principle and superexponential
convergence in probability to show that a functional large deviation principle
for a sequence of stochastic processes implies a corresponding functional large
deviation principle for an associated sequence of first-passage-time or inverse
processes. Large deviation principles are established for both inverse
processes and centered inverse processes, based on corresponding results for
the original process. We apply these results to obtain functional large
deviation principles for renewal processes and superpositions of independent
renewal processes.
Publié le : 1997-05-14
Classification:
Large deviations,
large deviation principle,
Skorohod topologies,
contraction principle,
first passage times,
inverse processes,
counting processes,
renewal processes,
superpositions of renewal processes,
60F10,
60G55,
60K05
@article{1034625336,
author = {Puhalskii, Anatolii A. and Whitt, Ward},
title = {Functional large deviation principles for first-passage-time
processes},
journal = {Ann. Appl. Probab.},
volume = {7},
number = {1},
year = {1997},
pages = { 362-381},
language = {en},
url = {http://dml.mathdoc.fr/item/1034625336}
}
Puhalskii, Anatolii A.; Whitt, Ward. Functional large deviation principles for first-passage-time
processes. Ann. Appl. Probab., Tome 7 (1997) no. 1, pp. 362-381. http://gdmltest.u-ga.fr/item/1034625336/