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Biometrika 1970 57(1):129-139; doi:10.1093/biomet/57.1.129
© 1970 by Biometrika Trust
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A central limit theorem for absorbing Markov chains

JANE P. MATTHEWS

University of Sheffield

A central limit theorem is obtained for a sequence of random variables defined on a finite absorbing Markov chain, conditional on absorption not having taken place. The transition count for such a chain when suitably scaled is found to follow a multivariate normal distribution asymptotically. In the case where the transition probability matrix of the chain is a function of a single parameter {alpha}, a consistent estimator for {alpha} is found; this estimator is asymptotically normally distributed about the true value of {alpha}. The result is illustrated by a simulation study of a genetic model of Moran, for the case of one-way mutation in a population of gametes.


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