Question: 1. Problem 15.29 Let {Xn} be a Markov chain with no two disjoint closed sets and state space I ={1,2,...,N}. Suppose that the Markov chain

1. Problem 15.29 Let {Xn} be a Markov chain with no two disjoint closed sets and state space I ={1,2,...,N}. Suppose that the Markov chain is doubly stochastic; that is, for each of the columns of the matrix of one-step transition probabilities the column elements sum to one. Verify that the Markov chain has the unique equilibrium distribution πj = 1 N

for all j.

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