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On -convergence of Markov chains

Published online by Cambridge University Press:  24 October 2008

D. J. Aldous
D. J. Aldous
Affiliation:
Department of Statistics, University of California, Berkeley, California 94720
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Extract

Let I be a countable set, with discrete topology, and let X = (Xn), Y = (Yn) be stationary stochastic processes taking values in I. To a probabilist, the natural topology on processes (strictly speaking, on distributions of processes) is weak convergence:

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 2 , September 1981 , pp. 331 - 333
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

REFERENCES

(1)Ellis, M. H.Distances between two-state Markov processes attainable by Markov joinings. Trans. Amer. Math. Soc. 241 (1978), 129–153.CrossRefGoogle Scholar
(2)Ellis, M. H.On Kamae's conjecture concerning the d-distance between two-state Markov processes. Ann. Probability 8 (1980), 372–376.CrossRefGoogle Scholar
(3)Ellis, M. H.Conditions for attaining d by a Markovian joining. Ann. Probability 8 (1980), 431–440.CrossRefGoogle Scholar
(4)Ornstein, D. S.An application of ergodic theory to probability theory. Ann. Probability 1 (1973), 43–65.CrossRefGoogle Scholar