Question: Lemma: Let (X0, X1, X2, . . .) be a Markov chain with state-space S = {1, 2, . . . , n} and transition

Lemma: Let (X0, X1, X2, . . .) be a Markov chain with state-space S = {1, 2, . . . , n} and transition matrix P.

Let w = (w1,w2, . . . ,wn) be a probability vector.

Then w is a limiting distribution for the Markov chain if and only if for any initial distribution (0), the distributions (t) satisfy (t) w as t .

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