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On idempotent D-norms

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  • Falk, Michael

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.

Suggested Citation

  • Falk, Michael, 2015. "On idempotent D-norms," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 283-294.
    • Handle: RePEc:eee:jmvana:v:139:y:2015:i:c:p:283-294
    DOI: 10.1016/j.jmva.2015.03.010
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    References listed on IDEAS

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    1. Wang, Yizao & Stoev, Stilian A., 2010. "On the association of sum- and max-stable processes," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 480-488, March.
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    Cited by:

    1. Hashorva, Enkelejd, 2018. "Representations of max-stable processes via exponential tilting," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2952-2978.
    2. Falk, Michael & Wisheckel, Florian, 2017. "Asymptotic independence of bivariate order statistics," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 91-98.
    3. Falk, Michael & Stupfler, Gilles, 2017. "An offspring of multivariate extreme value theory: The max-characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 85-95.

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