Loud Shot Noise

We consider problems involving large or loud values of the shot noise process X(t):=.i:.i.th(t..i),t.0, where h:[0,.).[0,.) is nonincreasing and (.i,i.0) is the sequence of renewal times of a renewal process. Results are obtained by extending the renewal sequence to all i.Z and considering the stationary sequence (.n) given by .n=.i.nh(.n..i). We show that .n has a thin tail in the sense that under broad circumstances Pr{.n>x+...n>x}.0 as x.., where .>0. We also show that Pr{max(.1,.,.n).un}.(Pr{.0.un})n.0 for real sequences (un) for which limsupnPr{.0>un}<..