Intricacies of Dependence between Components of Multivariate Markov Chains: Weak Markov Consistency and Markov Copulae

TL;DR

This paper explores the dependence structures in multivariate Markov chains, focusing on weak Markovian consistency and introducing weak Markov copulae to better understand component interactions.

Contribution

It characterizes weak Markovian consistency for finite Markov chains and introduces the concept of weak Markov copulae, advancing the theoretical understanding of component dependence.

Findings

Characterization of weak Markovian consistency for finite Markov chains

Introduction of weak Markov copulae concept

Analysis of dependence between components in multivariate chains

Abstract

This article continues our study of Markovian consistency and Markov copulae. In particular, we characterize the weak Markovian consistency for finite Markov chains. We discuss some aspects of dependence between the components of a multivariate Markov chain in the context of weak Markovian consistency and strong Markovian consistency. In this connection, we also introduce and discuss the concept of weak Markov copulae.