A Characterisation of Transient Random Walks on Stochastic Matrices with Dirichlet Distributed Limits. (June 2014) - McKinlay, S.
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.