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The rate of convergence of the vector of variances and covariances in non-homogeneous Markov systems

Published online by Cambridge University Press:  14 July 2016

P.-C. G. Vassiliou  and
G. Tsaklidis
P.-C. G. Vassiliou
Affiliation:
University of Thessaloniki
G. Tsaklidis*
Affiliation:
University of Thessaloniki
*
∗ Postal address for both authors: Statistics and Operations Research Section, Department of Mathematics, University of Thessaloniki, 54006 Thessaloniki, Greece.
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Abstract

The aims of this paper are twofold. The first is to study the rate of convergence of the sequence of vectors of expectations, variances and covariances in NHMS. It is proved that under certain conditions easily met in practice the rate is geometric. The second is to study the rate of convergence of the same sequence when the NHMS is under cyclic behaviour and it is also proved that the rate of convergence of the d subsequences (d being the period of the cycle) in which the sequence splits is geometric.

Keywords

STOCHASTIC POPULATION MODELSCYCLIC BEHAVIOUR OF NON-HOMOGENEOUS MARKOV SYSTEMSASYMPTOTIC VARIABILITY OF NON-HOMOGENEOUS MANPOWER SYSTEMSNON-HOMOGENEOUS MARKOV CHAINS
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 4 , December 1989 , pp. 776 - 783
Copyright
Copyright © Applied Probability Trust 1989 

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References

Bartholomew, D. J. (1971) The statistical approach to manpower planning. Statistician 20, 3–26.Google Scholar
Bartholomew, D. J. (1973) Stochastic Models for Social Processes, 2nd edn. Wiley, New York.Google Scholar
Bartholomew, D. J. (1982) Stochastic Models for Social Processes, 3rd edn. Wiley, New York.Google Scholar
Bartholomew, D. J. and Forbes, A. F. (1979) Statistical Techniques of Manpower Planning. Wiley, New York.Google Scholar
Conlisk, J. (1976) Interactive Markov chains. J. Math. Sociol. 4, 157–185.Google Scholar
Feichtinger, G. (1976) On the generalization of stable age distributions to Gani-type person-flow models. Adv. Appl. Prob. 8, 433–445.Google Scholar
Feichtinger, G. and Mehlmann, A. (1976) The recruitment trajectory corresponding to particular stock sequences in Markovian person-flow models. Math. Operat. Res. 1, 175–184.Google Scholar
Gani, J. (1963) Formula for projecting enrolments and degrees awarded in universities. J. R. Statist. Soc. A 126, 400–409.Google Scholar
Huang, C., Isaacson, L. D. and Vinograde, B. (1976) The rate of convergence of certain nonhomogeneous Markov chains. Z. Wahrscheinlichkeitsth. 35, 141–146.Google Scholar
Iosifescu, M. (1980) Finite Markov Processes and their Applications. Wiley, New York.Google Scholar
Mehlmann, A. (1977) A note on the limiting behaviour of discrete time markovian manpower models with inhomogeneous Poisson input. J. Appl. Prob. 14, 611–613.CrossRefGoogle Scholar
Pollard, J. H. (1966) On the use of direct product matrix in analysing certain stochastic population models. Biometrika 53, 397–415.Google Scholar
Pollard, J. H. (1973) Mathematical Models for the Growth of Human Population. Cambridge University Press.Google Scholar
Vassiliou, P.-C. G. (1981a) On the limiting behaviour of a non-homogeneous Markov chain model in manpower systems. Biometrika 68, 557–561.Google Scholar
Vassiliou, P.-C. G. (1981b) Stability in a non-homogeneous Markov chain model in manpower systems. J. Appl. Prob. 18, 924–930.CrossRefGoogle Scholar
Vassiliou, P.-C. G. (1982a) On the limiting behaviour of a non-homogeneous Markovian manpower model with independent Poisson input. J. Appl. Prob. 19, 433–438.CrossRefGoogle Scholar
Vassiliou, P.-C. G. (1982b) Asymptotic behaviour of Markov systems. J. Appl. Prob. 19, 851–857.Google Scholar
Vassiliou, P.-C. G. (1986) Asymptotic variability of nonhomogeneous Markov systems under cyclic behaviour. Eur. J. Operat. 27, 215–228.CrossRefGoogle Scholar
Vassiliou, P.-C. G. and Gerontidis, I. (1985) Variances and covariances of the grade sizes in manpower systems. J. Appl. Prob. 22, 583–597.Google Scholar