For a class of birth and death processes under a heavy traffic condition, the asymptotic behavior of functionals of their jumps is investigated. It is shown that, under suitable normalization, the functionals converge in law to a process that is the sum of a Brownian motion and a constant times the local time of a reflecting Brownian motion at zero. Some applications to queueing processes are presented.
Publié le : 1993-08-14
Classification:
Limit theorem,
functionals of jumps,
birth and death processes,
heavy traffic condition,
reflecting Brownian motion,
local time,
60F17,
60K25,
60H30
@article{1177005367,
author = {Yamada, Keigo and Hong, Sung Jo},
title = {A Limit Theorem for Functionals of Jumps of Birth and Death Processes under Heavy Traffic Condition},
journal = {Ann. Appl. Probab.},
volume = {3},
number = {4},
year = {1993},
pages = { 840-862},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005367}
}
Yamada, Keigo; Hong, Sung Jo. A Limit Theorem for Functionals of Jumps of Birth and Death Processes under Heavy Traffic Condition. Ann. Appl. Probab., Tome 3 (1993) no. 4, pp. 840-862. http://gdmltest.u-ga.fr/item/1177005367/