Consider the shot noise process X(t):¸=Σih(t-τi), t≥0, where h is a bounded positive non-increasing function supported on a finite interval, and the τi’s are the points of a renewal process η on [0,•). In this paper, the extremal properties of {X(t)} are studied. It is shown that these properties can be investigated in a natural way through a discrete-time process which records the states of {X(t)} at the points of η. The important special case where η is Poisson is treated in detail, and a domain-of-attraction result for the compound Poisson distribution is obtained as a by-product.
