Abstract
A representation for products of finite nonnegative matrices is given in terms of products of stochastic matrices and as a result Markov chain arguments are used to derive ratio limit properties. In particular, we obtain necessary and sufficient conditions for weak ergodicity and give a probabilistic proof of the Coale-Lopez theorem. In the general case, there are several sequences of sets of partitions of the state space corresponding to an associated nonhomogeneous Markov chain which lead to a number of ratio product limits. Asymptotic column proportionality, characteristic of weak ergodicity, may occur only inside each sequence of sets with one possible exception.
Citation
Harry Cohn. Olle Nerman. "On Products of Nonnegative Matrices." Ann. Probab. 18 (4) 1806 - 1815, October, 1990. https://doi.org/10.1214/aop/1176990650
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