On some extremes of mixing for Copula-based Markov chains

Abstract

This paper presents a new general construction of copula that includes some known families such as the Farlie-Gumbel-Morgenstern copula family. This general form of copula helps address extreme cases of mixing and justifies optimality of the results of Longla [1] and Longla [2] on mixing for copula-based Markov chains. Some examples are presented to show that the results can not be extended by weakening the assumptions. keywords Copula-based Markov chains, Mixing for Markov chains, ergodicity, Markov chain central limit theorem