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An extension to the renewal theorem and an application to risk theory. (English) Zbl 0876.60072
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.

MSC:
60K05 Renewal theory
60F10 Large deviations
62P05 Applications of statistics to actuarial sciences and financial mathematics
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