Convergence of Markov Chains

Abstract

We consider a Markov chain X with invariant distribution π and investigate conditions under which the distribution of Xnconverges to π as n→∞. Essentially it is necessary and sufficient that the state space of the chain cannot be decomposed into subspaces that the chain does not leave,or that are visited by the chain periodically; e.g., only for odd n or only for even n.