Limit Theorems for Maxima of Heavy-Tailed Terms with Random Dependent Weights

2000 Mathematics Subject Classification: Primary 60F17, 60G52, 60G70 secondary 60E07, 62E20.

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.

This research was partially supported by a Rackham faculty research fellowship at the University of Michigan, Ann Arbor and the NSF Grant DMS-0505747 at Boston University