Characterizations of Archimedean n-copulas

Proving the characetrization of Archimedean copulas via Dini derivatives

“…In [18], the author provides three characterizations of n-dimensional Archimedean copulas: algebraic, differential and diagonal. Our purpose in this note is to provide a new proof of Theorem 1.1 (Section 3) by using Dini derivatives, a known result of Lebesgue from Real Analysis (Section 2) -which allow to reconstruct a function from the Dini derivative D + f when this is finite -and a characterization of copulas given by Jaworski and Durante [5].…”