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Asymptotic periodicity of the variances and covariances of the state sizes in non-homogeneous Markov systems

Published online by Cambridge University Press:  14 July 2016

G. Tsaklidis  and
P.-C. G. Vassiliou
G. Tsaklidis
Affiliation:
University of Thessaloniki
P.-C. G. Vassiliou*
Affiliation:
University of Thessaloniki
*
∗ Postal address: Statistics and Operational Research Section, Mathematics Department, University of Thessaloniki, Thessaloniki, Greece.
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Abstract

In this paper we study the asymptotic periodicity of the sequence of means, variances and covariances of the state sizes of non-homogeneous Markov systems. It is proved that under the assumption that the sequence of the extended stochastic transition matrices converge to a matrix which is an irreducible stochastic matrix of period d, and all the matrices in this sequence have the same incidence matrix, then the sequence of means, variances and covariances splits into d subsequences which converge. Finally, we discuss the application of the present results in a manpower system.

Keywords

STOCHASTIC POPULATION MODELSASYMPTOTIC BEHAVIOUR ON NON-HOMOGENEOUS MANPOWER SYSTEMSNON-HOMOGENEOUS MARKOV CHAINS
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 1 , March 1988 , pp. 21 - 33
Copyright
Copyright © Applied Probability Trust 1988 

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