In applied probability one is often interested in the asymptotic
behavior of a certain quantity. If a regenerative phenomenon can be imbedded,
then one has the problem that the event of interest may have occurred but
cannot be observed at the renewal points. In this paper an extension to the
renewal theorem is proved which shows that the quantity of interest converges.
As an illustration an open problem in risk theory is solved.
Publié le : 1997-02-14
Classification:
Renewal theorem,
limit theorems,
large deviations,
risk theory,
ruin probabilities,
60K05,
60F10,
62P05
@article{1034625255,
author = {Schmidli, H.},
title = {An extension to the renewal theorem and an application to risk
theory},
journal = {Ann. Appl. Probab.},
volume = {7},
number = {1},
year = {1997},
pages = { 121-133},
language = {en},
url = {http://dml.mathdoc.fr/item/1034625255}
}
Schmidli, H. An extension to the renewal theorem and an application to risk
theory. Ann. Appl. Probab., Tome 7 (1997) no. 1, pp. 121-133. http://gdmltest.u-ga.fr/item/1034625255/