A central limit theorem for absorbing Markov chains

Jane P. Matthews

Biometrika, 1970, vol. 57, issue 1, 129-139

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.

Date: 1970
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