Published online by Cambridge University Press: 18 September 2020
In this chapter the concept of strong Markov consistency and the concept of weak Markov consistency for finite time-inhomogeneous multivariate Markov chains is introduced and studied. In particular, necessary and sufficient conditions for both types of Markov consistency are given. The main tool used here is the semimartingale characterization of finite Markov chains. In addition, operator interpretation of a sufficient condition for strong Markov consistency and a necessary condition for weak Markov consistency are provided. By definition, strong Markov consistency implies the weak Markov consistency. In this chapter we provide sufficient condition for the reverse implication to hold.