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VIII.—The Central Limit Theorem for a Convergent Non-homogeneous Finite Markov Chain*

Published online by Cambridge University Press:  14 February 2012

J. L. Mott
J. L. Mott
Affiliation:
Department of Mathematics, University of Edinburgh.
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Synopsis

The distribution of xn, the number of occurrences of a given one of k possible states of a non-homogeneous Markov chain {Pj} in n successive trials, is considered. It is shown that if Pn → P, a positive-regular stochastic matrix, as n → ∞ then the distribution about its mean of xn/n½ tends to normality, and that the variance tends to that of the corresponding distribution associated with the homogeneous chain {P}.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 65 , Issue 2 , 1959 , pp. 109 - 120
Copyright
Copyright © Royal Society of Edinburgh 1959

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References

References to Literature

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