基于 Bernstein Copula 函数的随机变量序列的 Max-Sum 局部等价式

数学物理学报 ›› 2024, Vol. 44 ›› Issue (4): 1110-1125.

• • 上一篇

基于 Bernstein Copula 函数的随机变量序列的 Max-Sum 局部等价式

明瑞星¹(),楼振瀚¹(),崔盛^2,^3,^*(),龚婵^2,³()

¹浙江工商大学统计与数学学院杭州 310018
²三峡大学理学院湖北宜昌 443002
³三峡数学研究中心湖北宜昌 443002

收稿日期:2023-12-01 修回日期:2024-04-29 出版日期:2024-08-26 发布日期:2024-07-26
通讯作者: *崔盛, E-mail: cuisheng@ctgu.edu.cn
作者简介:明瑞星, E-mail: rxming@zjgsu.edu.cn;楼振瀚, E-mail: lzh00214@163.com;龚婵, E-mail: 2556516736@qq.com
基金资助:
浙江省重点建设高校优势特色学科 (浙江工商大学统计学)、浙江工商大学“数字+” 学科建设管理项目“数据资产: 经济理论, 价值核算, 市场交易与政策创新(SZJ2022B004);浙江省统计科学研究基地项目高维情形下最小方差投资组合研究(22TJD02);宜昌市大学科学研究与应用项目(A21-3-018)

Local Max-sum Equivalence of Random Variables with Bernstein Copula

Ming Ruixing¹(),Lou Zhenhan¹(),Cui Sheng^2,^3,^*(),Gong Chan^2,³()

¹School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018
²Science College,China Three Gorges University, Hubei Yichang 443002
³Three Gorges Mathematical Research Center,China Three Gorges University, Hubei Yichang 443002

Received:2023-12-01 Revised:2024-04-29 Online:2024-08-26 Published:2024-07-26
Supported by:
Characteristic & Preponderant Discipline of Key Construction Universities in Zhejiang Province (Zhejiang Gongshang University–Statistics), the Collaborative Innovation Center of Statistical Data Engineering Technology & Application, Digital + Discipline Construction Project(SZJ2022B004);Research on Minimum Variance Portfolio of Zhejiang Statistical Science Research Base Project in High dimension(22TJD02);Scientific Research and Application Project of Universities in Yichang City(A21-3-018)

摘要/Abstract

摘要：

该文考虑一类具有局部长尾分布, 但不一定具有相同分布的随机变量序列, 其联合分布由 Bernstein copula 函数进行联系. 研究其部分和及其最大值的局部分布的渐近性质. 在假设诸随机变量服从局部次指数分布的条件下, 得到了 Max-Sum 局部等价性. 该等价性从局部和相依的角度描述了随机游动的一次大跳原理. 数值实验表明所得结果稳定可行.

关键词: Bernstein copula, Max-Sum 局部等价性, 局部次指数分布, 一次大跳原理

Abstract:

In this paper, we consider a sequence of non-negative dependent and not necessarily identically distributed random variables with local long-tailed marginal distributions and Bernstein copula and study the local asymptotic behavior of the tail of their partial sum and maximum. Then, under a suitable condition for local subexponentiality, we obtain the local max-sum equivalence. The result indicates that the big-jump principle of random walks remains valid in its local version under more general dependency assumptions. The numerical experimental results under different parameter settings further validate the stability and feasibility of the obtained results.

Key words: Bernstein copula, Local max-sum equivalence, Local subexponentiality, Principle of a single big jump

中图分类号:

O175.23

明瑞星, 楼振瀚, 崔盛, 龚婵. 基于 Bernstein Copula 函数的随机变量序列的 Max-Sum 局部等价式[J]. 数学物理学报, 2024, 44(4): 1110-1125.

Ming Ruixing, Lou Zhenhan, Cui Sheng, Gong Chan. Local Max-sum Equivalence of Random Variables with Bernstein Copula[J]. Acta mathematica scientia,Series A, 2024, 44(4): 1110-1125.

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参考文献 35

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基于 Bernstein Copula 函数的随机变量序列的 Max-Sum 局部等价式

Local Max-sum Equivalence of Random Variables with Bernstein Copula

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