Abstract
Based on an explicit representation of moments of hitting times for single death processes, the criteria on ergodicity and strong ergodicity are obtained. These results can be applied for an extended class of branching processes. Meanwhile, some sufficient and necessary conditions for recurrence and exponential ergodicity as well as extinction probability for the processes are presented.
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Acknowledgements
The author acknowledges the constructive discussion with Professor Mu-Fa Chen, Professor Yong-Hua Mao, Yue-Shuang Li, and Yan-Yan Yan. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11571043, 11771047, 11871008).
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Zhang, Y. Criteria on ergodicity and strong ergodicity of single death processes. Front. Math. China 13, 1215–1243 (2018). https://doi.org/10.1007/s11464-018-0722-z
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DOI: https://doi.org/10.1007/s11464-018-0722-z