Intricacies of Dependence between Components of Multivariate Markov   Chains: Weak Markov Consistency and Markov Copulae
  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. 
Tomasz R. Bielecki, Jacek Jakubowski and Mariusz Niew\k{e}g{\l}owski
math.PR