| Abstract: | Consider the shot noise process $X(t) coloneq Sigma _{i}h(t- tau _{i}), t geq 0$, where h is a bounded positive non-increasing function supported on a finite interval, and the $ tau _{i}$'s are the points of a renewal process $ eta$ on [0, infty). 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 $ eta$. The important special case where $ eta$ is Poisson is treated in detail, and a domain-of-attraction result for the compound Poisson distribution is obtained as a by-product. |
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