Extremes for shot noise processes with heavy tailed amplitudes

Extreme value results for a class of shot noise processes with heavy tailed amplitudes are considered. For a process of the form, , where { τ k } are the points of a renewal process and { A k } are i.i.d. with d.f. having a regularly varying tail, the limiting behavior of the maximum is determined. The extremal index is computed and any value in (0, 1) is possible. Two-dimensional point processes of the form are shown to converge to a compound Poisson point process limit. As a corollary to this result, the joint limiting distribution of high local maxima is obtained.

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