Convergence of distributions of integral functionals of extremal random functions

Abstract

We study the convergence of distributions of integral functionals of random processes of the formU _n (t)=b _n (Z _n (t)-a _n G(t)),t⃛T, where {X=X(t), t⃛T} is a random process,X _n ,n≥1, are independent copies ofX, andZ _n (t)=max_1≤k≤n X _k (t)