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Extremes

, Volume 14, Issue 3, pp 285–310 | Cite as

Extremes of independent Gaussian processes

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Abstract

For every n ∈ ℕ, let X 1n ,..., X nn be independent copies of a zero-mean Gaussian process X n  = {X n (t), t ∈ T}. We describe all processes which can be obtained as limits, as n→ ∞, of the process a n (M n  − b n ), where M n (t) =  maxi = 1,...,n X in (t), and a n , b n are normalizing constants. We also provide an analogous characterization for the limits of the process a n L n , where L n (t) =  min i = 1,...,n |X in (t)|.

Keywords

Extremes Gaussian processes Max-stable processes Hüsler–Reiss distributions 

AMS 2000 Subject Classifications

Primary—60G70; Secondary—60G15 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institut für Mathematische StochastikGeorg-August-Universität GöttingenGöttingenGermany

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