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Inverses of extremal processes

Published online by Cambridge University Press:  01 July 2016

Sidney I. Resnick
Sidney I. Resnick*
Affiliation:
Stanford University
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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 of Y while Y is 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 of Y-Λ at t = ∞ to behavior near t = 0. Some extensions of these ideas to sample sequences of maxima of i.i.d. random variables are carried out.

Keywords

EXTREMAL PROCESSESMAXIMAITERATED LOGARITHMADDITIVE PROCESSESRECORD VALUESINVERSES

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 2 , June 1974, pp. 392 - 406
Copyright
Copyright © Applied Probability Trust 1974 

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