Some functionals for copulas (Q808582)

As the authors point out, the theory of couplas, introduced by \textit{A. Sklar} [Kybernetika, Praha 9, 449-460 (1973; Zbl 0292.60036)], has been found to be of interest in describing the dependence between two or more random variables, which is given by their joint distribution function. The paper studies some functionals operating on the set of the copulas defined on \([0,1]^ n\) and determines the conditions under which these functionals are well defined. Then it provides some counterexamples describing the validity of these conditions. It also studies the fixed points (n-copulas) of these functionals and concludes with some open problems.