For long-range dependent infinitely divisible sequences with moderately heavy (log-normal-like) tails and dependence parameter β in (1/2,1), the normalized extremal process converges to a new non-Gumbel random sup-measure built from overlapping stable regenerative sets.
L\'evy processes , volume 121 of Cambridge Tracts in Mathematics
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Moderately Heavy Extreme Values under Extreme Long Range Dependence
For long-range dependent infinitely divisible sequences with moderately heavy (log-normal-like) tails and dependence parameter β in (1/2,1), the normalized extremal process converges to a new non-Gumbel random sup-measure built from overlapping stable regenerative sets.