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Open Access Article

Advances in International Applied Mathematics. 2022; 4: (2) ; 1-8 ; DOI: 10.12208/j.aam.20220008.

Stochastic and convergence rate estimation at Zolotarev distance and its application to limit theory
Zolotarev 距离下随机和收敛速率估计及其极限理论应用

作者: 贺钰淇 *

中国人民大学统计学院 北京;四川大学数学学院 四川成都

*通讯作者: 贺钰淇,单位:中国人民大学统计学院 北京;四川大学数学学院 四川成都;

发布时间: 2022-12-29 总浏览量: 16

摘要

随机和及其极限理论近几年在保险学、可靠性理论和金融应用中起到了十分重要的地位,因而对随机和在大数律下收敛速率的研究也十分关键。本文利用一种新的度量Zolotarev距离,研究随机和分布在Zolotarev距离上的收敛速率的上界,在此基础上将Korolev和Zeifman提出的混合泊松和推广到任意随机和的收敛速率,最后讨论Zolotarev距离下收敛性与依分布收敛之间的关系,并就相关随机树方面的应用作一些讨论。

关键词: Zolotarev距离;随机和;收敛速率

Abstract

In recent years, stochastic sum and its limit theory have played a very important role in insurance, reliability theory and financial applications, so the research on the convergence rate of stochastic sum under the law of large numbers is also very critical. In this paper, a new metric Zolotarev distance is used to study the upper bound of the convergence rate of random sum distribution over Zolotarev distance. On this basis, the mixed Poisson sums proposed by Korolev and Zeifman are extended to the convergence rate of arbitrary random sums. Finally, the relationship between convergence under Zolotarev distance and convergence in distribution is discussed, and some applications of related random trees are discussed.

Key words: Zolotarev distance; random sum; convergence rate

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引用本文

贺钰淇, Zolotarev 距离下随机和收敛速率估计及其极限理论应用[J]. 国际应用数学进展, 2022; 4: (2) : 1-8.