Title: The Markov product of copulas revisited
Authors: Wolfgang Trutschnig - University of Salzburg (Austria) [presenting]
Abstract: It is well known that the so-called star-product of two-dimensional copulas can equivalently be expressed in terms of the standard composition of the underlying Markov kernels. Building on this simple fact and on recent results we show that idempotence (i.e. invariance with respect to the star product) is a very rare property for copulas in commonly used classes. In particular, we prove that in the class of extreme-value copulas, in the class of Bernstein copulas, and in some special class of copulas represented by Lebesgue-measure-preserving transformations only the usual suspects - the product copula and minimum copula - are idempotent. Additionally, we prove a conjecture saying that the only idempotent strict Archimedean copula is the product copula.