Consider a system into which units having random magnitude enter at
arbitrary times and remain "active" (present in the system) for
random periods. Suppose units of high magnitude have stochastically greater
lifetimes (tend to stay active for longer periods) than units of low magnitude.
Of interest is the process ${\mu (t): t \geq 0}$ where $\mu (t)$ denotes the
average magnitude of all units active at time t. We give conditions
which guarantee the convergence of $\mu (t)$ and we determine the form of the
limit. Some related processes are also studied.
Publié le : 1997-02-14
Classification:
SLLN,
random deletion,
sample means,
60F15,
60G17
@article{1034625258,
author = {Rothmann, Mark D. and Russo, Ralph P.},
title = {A law of large numbers on randomly deleted sets},
journal = {Ann. Appl. Probab.},
volume = {7},
number = {1},
year = {1997},
pages = { 170-182},
language = {en},
url = {http://dml.mathdoc.fr/item/1034625258}
}
Rothmann, Mark D.; Russo, Ralph P. A law of large numbers on randomly deleted sets. Ann. Appl. Probab., Tome 7 (1997) no. 1, pp. 170-182. http://gdmltest.u-ga.fr/item/1034625258/