Extreme value theory for suprema of random variables with regularly varying tail probabilities
Let \(\{z_ i\}\) (i\(\in I)\) be a sequence of i.i.d. random variables with d.f. F(x) where \(1-F(x)=x^{-\alpha}L(x)\), L(x) slowly varying. Among other less important results it is shown that: a) Prob\(\{\) \(\sup_{i}c_ iz_ i>x\}\sim x^{-\alpha}L(x)\sum c_ i^{\alpha}\) as \(x\to +\infty\) under some restrictions; b) the two dimensional point process \(\{(j/n,(a_ nX_ i)^{- \alpha}\}\) with \(X_ n=\sup_{i}c_ iZ_{n-i}\) is shown to have a limit.
scientific article; zbMATH DE number 3965082