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Cyclic behaviour and asymptotic stability of non-homogeneous Markov systems

Published online by Cambridge University Press:  14 July 2016

P.-C. G. Vassiliou
Affiliation:
University of Thessaloniki

Abstract

In this paper we study the cyclic behaviour of non-homogeneous Markov systems, i.e. the behaviour of the system under the assumption of periodic sequences of transition matrices, input probabilities, output probabilities and total numbers in the system. We provide a general theorem for the limiting structure of such a system under the cyclic behaviour. We also study the asymptotic stability of non-homogeneous Markov systems and theorems are given which characterize asymptotic stability. An application of the above results is given for a British firm, BS.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

Part of this research was carried out while the author was at Imperial College, London.

References

Bartholomew, D. J. (1971) The statistical approach to manpower planning. Statistician 20, 326.CrossRefGoogle 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 for Manpower Planning. Wiley, New York.Google Scholar
Conlisk, J. (1976) Interactive Markov chains. J. Math. Sociol. 4, 157185.CrossRefGoogle Scholar
Conlisk, J. (1978) A stability theorem for an interactive Markov chain. J. Math. Sociol. 6, 163168.CrossRefGoogle Scholar
Feichtinger, G. (1976) On the generalization of stable age distributions to Gani-type person flow models. Adv. Appl. Prob. 8, 433445.CrossRefGoogle Scholar
Feichtinger, G. and Mehlmann, A. (1976) The recruitment trajectory corresponding to particular stock sequences in Markovian person flow models. Math. Operat. Res. 1, 175184.CrossRefGoogle Scholar
Gani, J. (1963) Formulae for projecting enrolments and degrees awarded in universities. J. R. Statist. Soc. A 126, 400409.Google Scholar
Gantmacher, F. R. (1959) Applications of the Theory of Matrices. Interscience Publishers, New York.Google Scholar
Iosifescu, M. (1980) Finite Markov Processes and their Applications. Wiley, New York.Google Scholar
Nikaido, H. (1968) Convex Structures and Economic Theory. Academic Press, New York.Google Scholar
Vassiliou, P.-C. G. (1981) Stability in a non-homogeneous Markov chain model in manpower systems. J. Appl. Prob. 18, 924930.CrossRefGoogle Scholar
Vassiliou, P.-C. G. (1982) Asymptotic behaviour of Markov systems. J. Appl. Prob. 19, 851857.CrossRefGoogle Scholar
Young, A. and Vassiliou, P.-C. G. (1974) A non-linear model on the promotion of staff. J. R. Statist. Soc. A 137, 584595.CrossRefGoogle Scholar

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