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A Characterisation of Transient Random Walks on Stochastic Matrices with Dirichlet Distributed Limits
Published online by Cambridge University Press: 19 February 2016
Abstract
We characterise the class of distributions of random stochastic matrices X with the property that the products X(n)X(n − 1) · · · X(1) of independent and identically distributed copies X(k) of X converge almost surely as n → ∞ and the limit is Dirichlet distributed. This extends a result by Chamayou and Letac (1994) and is illustrated by several examples that are of interest in applications.
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