Stationary probability vectors of higher-order Markov chains

We consider the higher-order Markov chain, and characterize the second order Markov chains admitting every probability distribution vector as a stationary vector. The result is used to construct Markov chains of higher-order with the same property. We also study conditions under which the set of stationary vectors of the Markov chain has a certain affine dimension. (C) 2014 Elsevier Inc. All rights reserved.