Remarks on the speed of convergence of mixing coefficients and applications

TL;DR

This paper investigates the convergence rates of dependence coefficients in copula-based Markov chains, providing new tools and conditions for exponential mixing, with applications to Metropolis-Hastings algorithms.

Contribution

It introduces novel methods to assess convergence rates of mixing coefficients and establishes conditions for exponential mixing in copula-based Markov chains, including Metropolis-Hastings.

Findings

Provided new tools for checking convergence rates

Established conditions for exponential $ ho$-mixing, $eta$-mixing, and $$-mixing

Improved previous results on mixtures of copulas

Abstract

In this paper, we study dependence coefficients for copula-based Markov chains. We provide new tools to check the convergence rates of mixing coefficients of copula-based Markov chains. We study Markov chains generated by the Metropolis-hastings algorithm and give conditions on the proposal that ensure exponential $\rho$-mixing, $\beta$-mixing and $\phi$-mixing. A general necessary condition on symmetric copulas to generate exponential $\rho$-mixing or $\phi$-mixing is given. At the end of the paper, we comment and improve some of our previous results on mixtures of copulas.