Consider an irreducible finite Markov chain with states 0, 1, . . . , N. (a) Starting
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Consider an irreducible finite Markov chain with states 0, 1, . . . , N.
(a) Starting in state i, what is the probability the process will ever visit state j? Explain!
(b) Let xi = P{visit state N before state 0|start in i}. Compute a set of linear equations that the xi satisfy, i = 0, 1, . . . , N.
(c) If
jjPij = i for i = 1, . . . , N − 1, show that xi = i/N is a solution to the equations in part (b).
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