Question: A birth- and death process has transition rates [lambda_{j}=(j+1) lambda text { and } mu_{j}=j^{2} mu ; j=0,1, ldots ; 0

A birth- and death process has transition rates

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

Confirm that this process has a stationary state distribution and determine it.

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