Birth-death processes on trees (Q625923)

This paper develops earlier work of \textit{S. Yan} and \textit{M. Chen} [Chin. Ann. Math., Ser. B 7, 90--110 (1986; Zbl 0596.60074)] and \textit{B. Wu} and \textit{Y.-H. Zhang} [J. Appl. Prob. 44, No. 1, 226--237 (2007; Zbl 1133.60345)] in the setting of the positive integers to study some birth-death processes on trees. The lack of a total order restricts what can be done, and here two different birth-death processes are constructed for which computable criteria can be found for recurrence, ergodicity, and other attributes. Upper and lower bounds are found for the Dirichlet eigenvalue.