Is it possible that a Markov chain is irreducible and aperiodic but without invariant distribution or without an invariant measure? Could someone give examples?
2026-03-28 23:58:44.1774742324
Irreducible and aperiodic Markov chain without invariant distribution/measure
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It is not clear if your state space is finite or not. If it is finite then stationary distribution exists. Otherwise, the MC need not be persistent and stationary distribution need not exist. Plenty of examples can be found in Karlin and Taylor’s book.