Question: S Birth-and-death processes. Let be a stochastic matrix on E D ZC. Suppose that .x; y/ > 0 if and only if either x

S Birth-and-death processes. Let … be a stochastic matrix on E D ZC. Suppose that

….x; y/ > 0 if and only if either x 1 and jx yj D 1, or x D 0 and y 1. Find a necessary and sufficient condition on … under which … has a stationary distribution ˛. If ˛

exists, express it in terms of the entries of ….

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