Markov product invariance in classes of bivariate copulas characterized by univariate functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:501

Article

Sanchez, J. Fernandez¹  Trutschnig, W.²  Tschimpke, M.² 

[1] Univ Almeria, Grp Invest Anal Matemat, Carretera Sacramento S-N, Almeria 04120, Spain

[2] Univ Salzburg, Dept Math, Hellbrunnerstr 34, A-5020 Salzburg, Austria

关键词: Copula;    Markov product;    Star product;    Invariance;   

DOI  :  10.1016/j.jmaa.2021.125184

来源: Elsevier

【 摘 要 】

We extend and sharpen some results in the literature concerning the notion of Markov product idempotence in some well-known classes of copulas. Focusing on families of copulas which are characterized by univariate functions we show that in the class of extreme-value copulas, in the class of diagonal copulas and in some special class of copulas represented by measure-preserving transformations only the usual suspects (if contained in the class) are idempotent, namely the product copula pi and minimum copula M. Additionally, we prove a conjecture going back to Albanese and Sempi in 2016 saying that the only idempotent Archimedean copula is the product copula pi. (C) 2021 The Author(s). Published by Elsevier Inc.

【 授权许可】

Free