On idempotent D-norms

JOURNAL OF MULTIVARIATE ANALYSIS

卷:139

Article

Falk, Michael

关键词: Multivariate extreme value theory;    Max-stable distributions;    Max-stable random vectors;    D-norm;    Generator of D-norm;    Idempotent D-norm;    D-norm track;   

DOI  :  10.1016/j.jmva.2015.03.010

来源: Elsevier

【 摘 要 】

Replacing the spectral measure by a random vector Z allows the representation of a maxstable distribution on R-d 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free