Perturbations of copulas and Mixing properties

Abstract

This paper explores the impact of perturbations of copulas on the dependence properties of the Markov chains they generate. We consider Markov chains generated by perturbed copulas. Results are provided for the mixing coefficients $\beta_n$, $\psi_n$ and $\phi_n$. Several results are provided on mixing for the considered perturbations. New copula functions are provided in connection with perturbations of variables that induce other types of perturbation of copulas not considered in the literature.