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

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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.

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Acknowledgements

The author acknowledges the constructive discussion with Professors Mu-Fa Chen, Yong-Hua Mao, and Yutao Ma, and thanks the anonymous referees for their very valuable suggestions and careful reading of the draft, which greatly improved the quality of the paper. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11571043, 11771047, 11871008).

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Authors and Affiliations

  1. Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Yuhui Zhang

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  1. Yuhui Zhang
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Correspondence to Yuhui Zhang.

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Zhang, Y. Moments of first hitting times for birth-death processes on trees. Front. Math. China 14, 833–854 (2019). https://doi.org/10.1007/s11464-019-0784-6

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  • DOI: https://doi.org/10.1007/s11464-019-0784-6

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