weighted maxima random weights limit theorems extremal Fr echet process
Issue Date:
2007
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Pliska Studia Mathematica Bulgarica, Vol. 18, No 1, (2007), 361p-378p
Abstract:
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.
