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On non-dissipative Markov chains

Published online by Cambridge University Press:  24 October 2008

J. G. Mauldon
J. G. Mauldon
Affiliation:
Corpus Christi CollegeOxford
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Extract

Consider a Markov chain with an enumerable infinity of states, labelled 0, 1, 2, …, whose one-step transition probabilities pij are independent of time. Then

I write

and, departing slightly from the usual convention,

Then it is known ((1), pp. 324–34, or (6)) that the limits πij always exist, and that

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 4 , October 1957 , pp. 825 - 835
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCES

(1)Feller, W.An introduction to probability theory and its applications, vol. 1 (New York, 1950).Google Scholar
(2)Foster, F. G.Markoff chains with an enumerable number of states and a class of cascade processes. Proc. Camb. Phil. Soc. 47 (1951), 77–85.CrossRefGoogle Scholar
(3)Foster, F. G.On Markov chains with an enumerable infinity of states. Proc. Camb. Phil. Soc. 48 (1952), 587–91.CrossRefGoogle Scholar
(4)Kendall, D. G.On non-dissipative Markoff chains with an enumerable infinity of states. Proc. Camb. Phil. Soc. 47 (1951), 633–4.CrossRefGoogle Scholar
(5)Lévy, P.Théorie de l'addition des variables aléatoires (Paris, 1937).Google Scholar
(6)Yosida, K. and Kakutani, S.Markoff process with an enumerable infinite number of possible states. Jap. J. Math. 16 (1939), 47–55.CrossRefGoogle Scholar