Question: (Detailed balance for three state chains). Consider a chain with state space f1; 2; 3g in which q.i; j / > 0 if i

(Detailed balance for three state chains). Consider a chain with state space f1; 2; 3g in which q.i; j / > 0 if i ¤ j and suppose that there is a stationary distribution that satisfies the detailed balance condition.

(a) Let .1/ D

c. Use the detailed balance condition between 1 and 2 to find .2/ and between 2 and 3 to find .3/. (b)What conditions on the rates must be satisfied for there to be detailed balance between 1 and 3?

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