Ergodic decomposition of Markov chains Original Research Article

We explicitly find the spectral decomposition, when it exists, of a Markov operator P* : image1 → image1 using the asymptotic periodicity of the associated infinite Markov matrix. We give a simple condition under which an infinite Markov matrix is asymptotically periodic. We also determine the set of P*-invariant distributions in image1 and the set of P*-ergodic distributions.