WEAK LIMIT RESULTS FOR THE EXTREMES OF A CLASS OF SHOT-NOISE PROCESSES

Shot noise processes form an important class of stochastic processes m odeling phenomena which occur as shocks to a system and with effects t hat diminish over time. In this paper we present extreme value results for two cases - a homogeneous Poisson process of shocks and a non-hom ogeneous Poisson process with periodic intensity function. Shocks occu r with a random amplitude having either a gamma or Weibull density and dissipate via a compactly supported impulse response function. This w ork continues work of Hsing and Teugels (1989) and Doney and O'Brien ( 1991) to the case of random amplitudes.