Question

In what case do markov chains not have a stationary distribution?

Answer 1

In this case, transition matrix has no stationary distribution, hence there does not exst a limiting distribution. Then for all , is a stationary distribution for . We have two closed irreducible sets . As another example, consider the disjoint union of one absorbing state, and a two or three state periodic chain

Answer 2

In this case, transition matrix has no stationary distribution, hence there does not exst a limiting distribution. Then for all , is a stationary distribution for . We have two closed irreducible sets . As another example, consider the disjoint union of one absorbing state, and a two or three state periodic chain.