Question: Let E be finite and a stochastic matrix on E. Show that satisfies the assumptions of the ergodic theorem (6.13) if and only

Let E be finite and … a stochastic matrix on E. Show that … satisfies the assumptions of the ergodic theorem (6.13) if and only if … is irreducible and aperiodic in the sense that for one (and thus all) x 2 E the greatest common divisor of the set ¹k 1 W …k.x; x/ > 0º is 1.

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