Perturbations of copulas and Mixing properties

TL;DR

This paper investigates how perturbing copulas affects the dependence and mixing properties of the Markov chains they generate, introducing new copula functions related to variable perturbations.

Contribution

It provides new results on mixing coefficients for perturbed copulas and introduces novel copula functions linked to variable perturbations.

Findings

Analysis of mixing coefficients $eta_n$, $\psi_n$, $\phi_n$ for perturbed copulas

New copula functions related to variable perturbations

Results on how perturbations influence dependence 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.