Open Access
February 1997 An extension to the renewal theorem and an application to risk theory
H. Schmidli
Ann. Appl. Probab. 7(1): 121-133 (February 1997). DOI: 10.1214/aoap/1034625255


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.


Download Citation

H. Schmidli. "An extension to the renewal theorem and an application to risk theory." Ann. Appl. Probab. 7 (1) 121 - 133, February 1997.


Published: February 1997
First available in Project Euclid: 14 October 2002

zbMATH: 0876.60072
MathSciNet: MR1428752
Digital Object Identifier: 10.1214/aoap/1034625255

Primary: 60K05
Secondary: 60F10 , 62P05

Keywords: large deviations , limit theorems , Renewal theorem , Risk theory , ruin probabilities

Rights: Copyright © 1997 Institute of Mathematical Statistics

Vol.7 • No. 1 • February 1997
Back to Top