A characterisation of transient random walks on stochastic matrices with Dirichlet distributed limits

Shaun McKinlay

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arXiv · 1212.4975

A characterisation of transient random walks on stochastic matrices with Dirichlet distributed limits

Shaun McKinlay

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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 i.i.d. copies $X(k)$ of $X$ converge a.s. as $n \rightarrow \infty$ 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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Shaun McKinlay. 2012-12-20. A characterisation of transient random walks on stochastic matrices with Dirichlet distributed limits. https://arxiv.org/abs/1212.4975

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