Title: Extremal clustering under moderate long range dependence and moderately heavy tails
Authors: Gennady Samorodnitsky - Cornell University (United States) [presenting]
Abstract: The purpose is to study the clustering of the extremes in a stationary sequence with subexponential tails in the maximum domain of attraction of the Gumbel. We obtain functional limit theorems in the space of random sup-measures and in the space D(0,infty). The limits have the Gumbel distribution if the memory is only moderately long. However, as our results demonstrate rather strikingly, the``heuristic of a single big jump'' could fail even in a moderately long-range dependence setting. As the tails become lighter, the extremal behavior of a stationary process may depend on multiple large values of the driving noise.