TWO TYPES OF MARKOV PROPERTY

Arkadiusz Kasprzyk

Władysław Szczotka

Abstract: 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.

Key words and phrases: Markov chains in the strict sense and in the wide sense, linear
prediction, covariance function, cyclostationary distribution, periodically correlated
process.