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

Shaun McKinlay

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

Probability 2014-12-05 v1

Authors: Shaun McKinlay

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.

Keywords

random walk in random environment random walks probability distribution

Cite

@article{arxiv.1212.4975,
  title  = {A characterisation of transient random walks on stochastic matrices with Dirichlet distributed limits},
  author = {Shaun McKinlay},
  journal= {arXiv preprint arXiv:1212.4975},
  year   = {2014}
}

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