For a discrete-time Markov chain,
- Is it right that there are no more than one limiting distribution, i.e., limiting distribution is unique if any?
- If the chain has more than one recurrence irreducible classes, then is it right that the limiting distribution does not exist?
- If the chain has only one recurrence class, does existence of transient states not affect the existence of a limiting distribution?
- When both limiting and stationary distributions exist, is it possible there is some stationary distribution that is not a limiting distribution?
- If interpreting the limiting distribution as limit of the distribution of $X_n$, in what sense does the sequence of distribution measures converge?
Thanks and regards!