Inverses of extremal processes

Abstract

The inverse of an extremal process {Y(t),t≧ 0} is an additive process whose Lévy measure can be computed. This measure controls among other things the Poisson number of jumps ofYwhileYis in the vertical window (c, d]. A simple transformation of the inverse of the extremal process governed by Λ (x) = exp{–e–x} is also extremal-Λ (x) and this fact enables one to relate behavior ofY-Λ att= ∞ to behavior neart= 0. Some extensions of these ideas to sample sequences of maxima of i.i.d. random variables are carried out.