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Moments of first hitting times for birth-death processes on trees. (English) Zbl 1472.60144

Summary: An explicit and recursive representation is presented for moments of the first hitting times of birth-death processes on trees. Based on that, the criteria on ergodicity, strong ergodicity, and \(\ell \)-ergodicity of the processes as well as a necessary condition for exponential ergodicity are obtained.

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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