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Uniform coupling of non-homogeneous Markov chains

Published online by Cambridge University Press:  14 July 2016

David Griffeath
David Griffeath*
Affiliation:
Cornell University
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Abstract

The Markov-Dobrushin condition for (weak) ergodicity of non-homogeneous discrete-time Markov chains, and an analogous criterion for continuous chains, are derived by means of coupling techniques.

Keywords

WEAK ERGODICITYERGODIC COEFFICIENTNON-HOMOGENEOUS MARKOV CHAINSCOUPLING
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 4 , December 1975 , pp. 753 - 762
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Dobrushin, R. L. (1956) Central limit theorem for nonstationary Markov chains. Theor. Prob. Appl. 1, 65–80; 329–383.CrossRefGoogle Scholar
[2] Dobrushin, R. L. (1971) Markov processes with a large number of locally interacting components. Probl. Peredaci Inform. 7, 70–87.Google Scholar
[3] Doeblin, W. (1938) Exposé de la théorie des chaînes simples constantes de Markov à un nombre fini d'états. Rev. Math, de l'Union Interbalkanique 2, 77–105.Google Scholar
[4] Griffeath, D. (1975) Ergodic theorems for graph interactions. Adv. Appl. Prob. 7, 179–194.CrossRefGoogle Scholar
[5] Griffeath, D. (1975) A maximal coupling for Markov chains. Z. Wahrscheinlichkeitsth. 31, 95–106.CrossRefGoogle Scholar
[6] Griffeath, D. (1975) Partial coupling and loss of memory for Markov chains. To appear.CrossRefGoogle Scholar
[7] Hajnal, J. (1958) Weak ergodicity in nonhomogeneous Markov chains. Proc. Camb. Phil. Soc. 54, 233–246.CrossRefGoogle Scholar
[8] Harris, T. E. (1974) Contact interactions on a lattice. Ann. Prob. 2, 969–988.CrossRefGoogle Scholar
[9] Holley, R. and Liggett, T. (1975) Ergodic theorems for weakly interacting particle systems and the voter model. To appear.CrossRefGoogle Scholar
[10] Iosifescu, M. (1966) Conditions nécessaires et suffisantes pour l'ergodicité uniforme des chaînes de Markoff variables et multiples. Rev. Roumaine Math. Pures Appl. 11, 325–330.Google Scholar
[11] Iosifescu, M. (1972) On two recent papers on ergodicity in nonhomogeneous Markov chains. Ann. Math. Statist. 43, 1732–1736.CrossRefGoogle Scholar
[12] Kingman, J. F. C. (1975) Geometrical aspects of the theory of nonhomogeneous Markov chains. Math. Proc. Camb. Phil. Soc. 77, 171–183.CrossRefGoogle Scholar
[13] Markov, A. A. (1907) Investigation of an important case of dependent trials. Izv. Akad. Nauk SPB 6, 61–80.Google Scholar
[14] Paz, A. (1970) Ergodic theorems for infinite probabilistic tables. Ann. Math. Statist. 41, 539–550.CrossRefGoogle Scholar
[15] Seneta, E. (1973) On the historical development of the theory of finite inhomogeneous Markov chains. Proc. Camb. Phil. Soc. 74, 507–513.CrossRefGoogle Scholar
[16] Seneta, E. (1973) Non-negative Matrices. Wiley, London.Google Scholar
[17] Vasershtein, L. N. (1969) Markov processes on countable product spaces, describing large systems of automata. Probl. Peredaci Inform. 3, 64–72.Google Scholar