13. A transition probability matrix is said to be doubly stochastic if the sum over each...

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13. A transition probability matrix Ñ is said to be doubly stochastic if the sum over each column equals one; that is,

ÓÑõ= for ally If such a chain is irreducible and aperiodic and consists of M + 1 states 0, 1 , . . . , M, show that the limiting probabilities are given by

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