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Extremes of independent Gaussian processes

Extremes volume 14, pages285–310(2011)Cite this article

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)|.

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Affiliations

  1. Institut für Mathematische Stochastik, Georg-August-Universität Göttingen, Goldschmidtstraße 7, 37077, Göttingen, Germany

    Zakhar Kabluchko

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  1. Zakhar Kabluchko
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Correspondence to Zakhar Kabluchko.

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Kabluchko, Z. Extremes of independent Gaussian processes. Extremes 14, 285–310 (2011). https://doi.org/10.1007/s10687-010-0110-x

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Keywords

  • Extremes
  • Gaussian processes
  • Max-stable processes
  • Hüsler–Reiss distributions

AMS 2000 Subject Classifications

  • Primary—60G70; Secondary—60G15