On Idempotent D-Norms

الأصل · EN

Replacing the spectral measure by a random vector allows the representation of a max-stable distribution on ᵈ with standard negative margins via a norm, called D-norm, whose generator is. The set of D-norms can be equipped with a commutative multiplication type operation, making it a semigroup with an identity element. This multiplication leads to idempotent D-norms. We characterize the set of idempotent D-norms. Iterating the multiplication provides a track of D-norms, whose limit exists and is again a D-norm. If this iteration is repeatedly done on the same D-norm, then the limit of the track is idempotent.