Check whether or under what restrictions a birth- and death process with transition rates [lambda_{j}=frac{j+1}{j+2} lambda text

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Check whether or under what restrictions a birth- and death process with transition rates

\[\lambda_{j}=\frac{j+1}{j+2} \lambda \text { and } \mu_{j}=\mu ; j=0,1, \ldots\]

has a stationary state distribution.

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