Two types of Markov property

• Autorzy: Kasprzyk A. , Szczotka W.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Markov chain; Markov process in the strict sense; MP; Markov process in the wide sense; WM; linear prediction; covariance function; cyclostationary distribution; periodically correlated process

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2008
• Tom: Vol. 28, Fasc. 1
• Strony: 75--90
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Kasprzyk A.

• Institute of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Szczotka W.

• Institute of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [1] P. Brémaud, Markov Chains, Gibbs Fields, Monte Carlo Simulations and Queues, Springer, New York 1999.
• [2] J. L. Doob, Stochastic Processes, Wiley, New York 1953.
• [3] M. Iosifescu, Finite Markov Processes and Their Applications, Wiley, New York 1980.
• [4] C. D. Lai, First order autoregressive Markov processes, Stochastic Process. Appl. 7 (1978), pp. 65-72.
• [5] P. Lancaster, Theory of Matrices, Academic Press, New York 1969.
• [6] H. Minc, Nonnegative Matrices, Wiley, New York 1988.
• [7] J. F. Reynolds, On the autocorrelation and spectral functions of queues, J. Appl. Probab. 5 (1968), pp. 467-475.
• [8] J. F. Reynolds, Some theorems on the transient covariance of Markov chains, J. Appl. Probab. 9 (1972), pp. 214-218.
• [9] E. Seneta, Non-negative Matrices and Markov Chains, Springer, New York 1981.