Two Types of Markov Property

The paper gives some insight into the relations between two types of Markov processes – in the strict sense and in the wide sense – as well as into two aspects of periodicity. It concerns Markov processes with finite state space, the elements of which are complex numbers. Firstly it is shown that under some assumptions this space can be transformed in such a way that the resulting Markov process is also Markov in the wide sense. Next, sufficient conditions are given under which periodic homogeneous Markov chain is a periodically correlated process. 2000 AMS Mathematics Subject Classification: Primary: 60J10, 60J27; Secondary: 60G12.