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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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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DOI: https://doi.org/10.1007/s10687-010-0110-x