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High order moments of first hitting times for single death processes

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Abstract

We present an explicit and recursive representation for high order moments of the first hitting times of single death processes. Based on that, some necessary or sufficient conditions of exponential ergodicity as well as a criterion on ℓ-ergodicity are obtained for single death processes, respectively.

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Acknowledgements

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

    Yuhui Zhang & Xiaofeng Zhou

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  1. Yuhui Zhang
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  2. Xiaofeng Zhou
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Correspondence to Yuhui Zhang.

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Zhang, Y., Zhou, X. High order moments of first hitting times for single death processes. Front. Math. China 14, 1037–1061 (2019). https://doi.org/10.1007/s11464-019-0780-x

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  • DOI: https://doi.org/10.1007/s11464-019-0780-x

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