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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
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