an:01014231
Zbl 0876.60072
Schmidli, H.
An extension to the renewal theorem and an application to risk theory
EN
Ann. Appl. Probab. 7, No. 1, 121-133 (1997).
00039310
1997
j
60K05 60F10 62P05
renewal theorem; limit theorems; large deviations; risk theory; ruin probabilities
Summary: 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. 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.