On idempotent D-norms

Michael Falk

Journal of Multivariate Analysis, 2015, vol. 139, issue C, 283-294

Abstract: Replacing the spectral measure by a random vector Z allows the representation of a max-stable distribution on Rd with standard negative margins via a norm, called D-norm, whose generator is Z. 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.

Keywords: Multivariate extreme value theory; Max-stable distributions; Max-stable random vectors; D-norm; Generator of D-norm; Idempotent D-norm; D-norm track (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.jmva.2015.03.010

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