This paper studies limiting properties of discretely sampled Poisson shot noise processes. Versions of the law of large numbers and central limit theorem are derived under very general conditions. Examples demonstrating the utility of the results are included.

We examine the joint finite structure of extremes of the ARCH process and find an unexpected phenomenon: when assessing probabilities of failure during some finite time interval in the future, the extremal index seems not to be the object to look at. Two possible ramifications of this phenomenon are put forward.

Classes of life distributions based on the moment-generating-function order are investigated in this paper. It is shown firstly that the class ℳ is closed under both convex linear combination and geometric compounding. Secondly, the class NBUmg (new better than used in the moment-generating-function order) is proved to be closed under increasing star-shaped transformations. Finally, the interplay between the stochastic comparison of the excess lifetime of a renewal process and the NBUmg interarrivals is studied.