Conditional Markov Chains Part II: Consistency and Copulae

In this paper we continue the study of conditional Markov chains (CMCs) with finite state spaces, that we initiated in Bielecki, Jakubowski and Niew\k{e}g\l owski (2015). Here, we turn our attention to the study of Markov consistency and Markov copulae with regard to CMCs, and thus we follow up on the study of Markov consistency and Markov copulae for ordinary Markov chains that we presented in Bielecki, Jakubowski and Niew\k{e}g\l owski (2013).