Asymptotic expansions and precise deviations in the Kingman coalescent
Asymptotic expansions and precise deviations in the Kingman coalescent
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DOI：
10.1214/21-ecp375
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发表时间：
2021
影响因子：
0.5
通讯作者：
F. Gao;Yujing Wang;Youzhou Zhou
中科院分区：
文献类型：
--
作者：
F. Gao;Yujing Wang;Youzhou Zhou
本文研究了金曼聚结的小时间渐近行为。在中心极限定理中得到了Berry-Esseen界和Edgeworth展开式。此外，利用mod-φ收敛方法，我们还得到了精确大偏差和精确中偏差。最后，我们还得到了金曼合并的一个非渐近偏差不等式。
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 nonasymptotic deviation inequality for the Kingman coalescent.