We consider a storage process $X(t)$ having a compound Poisson process as input and general release rules, and a nonnegative additive functional $Z(t) = \int^t_0 f(X(s)) ds$. Under the situation that the input rate is equal to the maximal output rate, it is shown for a suitable class of functions of $f$ that an appropriate normalization of the process $Z(t)$ converges weakly to a process which is represented as a constant times the local time of a Bessel process at zero.
Publié le : 1985-05-14
Classification:
Storage process,
functional limit theorem,
local time of Bessel process,
60F17,
60J55,
60K30
@article{1176992999,
author = {Yamada, Keigo},
title = {A Limit Theorem for Nonnegative Additive Functionals of Storage Processes},
journal = {Ann. Probab.},
volume = {13},
number = {4},
year = {1985},
pages = { 397-413},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992999}
}
Yamada, Keigo. A Limit Theorem for Nonnegative Additive Functionals of Storage Processes. Ann. Probab., Tome 13 (1985) no. 4, pp. 397-413. http://gdmltest.u-ga.fr/item/1176992999/