. Using the dominated convergence for sums, show that a limiting distribution for a Markov chain (which need not be ergodic) is a stationary distribution. Give an example of a non-ergodic Markov chain...

. Using the dominated convergence for sums, show that a limiting distribution for a Markov chain (which need not be ergodic) is a stationary distribution. Give an example of a non-ergodic Markov chain with a stationary distribution that is not a limiting distribution.