On mixtures of copulas and mixing coefficients

We show that if the density of the absolutely continuous part of a copula is bounded away from zero on a set of Lebesgue measure 1, then that copula generates “lower ψψ-mixing” stationary Markov chains. This conclusion implies ϕϕ-mixing, ρρ-mixing, ββ-mixing and “interlaced ρρ-mixing”. We also provide some new results on the mixing structure of Markov chains generated by mixtures of copulas.