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A central limit theorem for absorbing Markov chains

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  • Jane P. Matthews

Abstract

SummaryA 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 α, a consistent estimator for α is found; this estimator is asymptotically normally distributed about the true value of α. 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.

Suggested Citation

  • Jane P. Matthews, 1970. "A central limit theorem for absorbing Markov chains," Biometrika, Biometrika Trust, vol. 57(1), pages 129-139.
    • Handle: RePEc:oup:biomet:v:57:y:1970:i:1:p:129-139.
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    File URL: http://hdl.handle.net/10.1093/biomet/57.1.129
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