Extremes of Independent Gaussian Processes

Abstract

For every $n\in \mathbb{N}$, let $X_{1n},...,X_{nn}$ be independent copies of a zero-mean Gaussian process $X_n=\{X_n(t),t\in T\}$. We describe all processes which can be obtained as limits, as $n\to \infty$, of the process $a_n(M_n-b_n)$, where $M_n(t)={\max }_{i=1,...,n}{X}_{in}(t)$ 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 $L_n(t)={\min }_{i=1,...,n}|X_{in}(t)|$.

19 pages