Extremes of independent Gaussian processes

Abstract

For every n ∈ ℕ, let X1n,..., Xnn be independent copies of a zero-mean Gaussian process Xn = {Xn(t), t ∈ T}. We describe all processes which can be obtained as limits, as n → ∞, of the process an(Mn - bn), where Mn(t) = maxi = 1,...,nXin(t), and an, bn are normalizing constants. We also provide an analogous characterization for the limits of the process anLn, where Ln(t) = min i = 1,...,n {pipe}Xin(t){pipe}. © 2010 Springer Science+Business Media, LLC.