Extremes of Independent Gaussian Processes
Abstract
For every 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)=i=1,...,n Xin(t) and an, bn are normalizing constants. We also provide an analogous characterization for the limits of the process anLn, where Ln(t)=i=1,...,n |Xin(t)|.
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