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Extremes of subexponential Lévy-driven random fields in the Gumbel domain of attraction
Ist Teil von
Extremes (Boston), 2022-03, Vol.25 (1), p.79-105
Ort / Verlag
New York: Springer US
Erscheinungsjahr
2022
Link zum Volltext
Quelle
EBSCOhost Business Source Ultimate
Beschreibungen/Notizen
We consider a spatial Lévy-driven moving average with an underlying Lévy measure having a subexponential right tail, which is also in the maximum domain of attraction of the Gumbel distribution. Assuming that the left tail is not heavier than the right tail, and that the integration kernel satisfies certain regularity conditions, we show that the supremum of the field over any bounded set has a right tail equivalent to that of the Lévy measure. Furthermore, for a very general class of expanding index sets, we show that the running supremum of the field, under a suitable scaling, converges to the Gumbel distribution.