Abstract
In this paper, we study the small-time asymptotic behavior of the Kingman coalescent. We obtain the Berry-Esseen bound and the Edgeworth expansion in the central limit theorem. Moreover, by the method of mod-ϕ convergence, we also obtain the precise large deviations and the precise moderate deviations. Last, we also obtain a non-asymptotic deviation inequality for the Kingman coalescent.
Acknowledgments
This work is supported by National Natural Science Foundation of China (Nos.11971361,11731012 and 11701570).
Citation
Fuqing Gao. Yujing Wang. Youzhou Zhou. "Asymptotic expansions and precise deviations in the Kingman coalescent." Electron. Commun. Probab. 26 1 - 11, 2021. https://doi.org/10.1214/21-ECP375
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