15 Markov Chains: Limiting Probabilities
15 MARKOV CHAINS: LIMITING PROBABILITIES 170 This is an irreducible chain, with invariant distribution π0 = π1 = π2 = 1 3 (as it is very easy to check). Moreover P2 = 0 0 1 1 0 0 0 1 0 , P3 = I, P4 = P, etc. Although the chain does spend 1/3 of the time at each state, the transition
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