Limit theorems for maxima of heavy-tailed terms with random dependent weights
Taqqu, Murad S.
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Citation (published version)Stilian Stoev, Murad S Taqqu. 2007. "Limit Theorems for Maxima of Heavy-Tailed Terms with Random Dependent Weights." Pliska Studia Mathematica Bulgarica, 2007, v. 18, pp. 361-378.
We study the general case when the weights Wj , j N can be dependent and in particular long-range dependent. Under mild tail and convergence conditions on the weights Wjs, we establish limit theorems for scaled versions of the process fMn(t)gt_0, as n ! 1. The limit processes are mixtures of extremal Frechet processes. The results are valid when the laws of the Uj’s belong to the normal domain of attraction of a Frechet distribution or to a sub-class of the general domain of attraction of a Frechet law.