The Condition of Regularity in Simple Markov Chains

Abstract

The paper generalizes a proof, and outlines an alternative to it, for the well-known theorem on the conditions of regularity in a simple Markov chain; this is that the necessary and sufficient conditions for a chain to be regular are that the latent root 1 of the stochastic matrix for the chain must be simple, and the remaining roots have moduli less than 1.