Semigroups of Binary Stochastic Matrices and Convergence of Nonhomogeneous Markov Chains

摘要

We give conditions which determine when a stochastic matrix can be written as a convex combination of binary stochastic matrices from a particular class of semigroups. Using the equivalence between convolution products of measures and products in the semigroup algebra of binary stochastic matrices, verifiable conditions based only on the entries in the individual transition matrices are given for the convergence of certain nonhomogeneous Markov chains.