Moments of first hitting times for birth-death processes on trees

Abstract

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 l-ergodicity of the processes as well as a necessary condition for exponential ergodicity are obtained.

Key words： Birth-death process on trees; ergodicity; hitting time; returning time

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