AN EXTENSION OF ZOLOTAREV'S PROBLEM AND SOME RELATED RESULTS

doi:10.1007/s10473-021-0513-6

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (5): 1619-1634.doi: 10.1007/s10473-021-0513-6

AN EXTENSION OF ZOLOTAREV'S PROBLEM AND SOME RELATED RESULTS

Tran Loc HUNG, Phan Tri KIEN

University of Finance and Marketing, 77 Nguyen Kiem Street, Phu Nhuan District, Ho Chi Minh City, Vietnam

收稿日期:2020-01-06 修回日期:2020-09-28 出版日期:2021-10-25 发布日期:2021-10-21
通讯作者: Tran Loc HUNG E-mail:tlhung@ufm.edu.vn
作者简介:Phan Tri KIEN,E-mail:phankien@ufm.edu.vn

AN EXTENSION OF ZOLOTAREV'S PROBLEM AND SOME RELATED RESULTS

Tran Loc HUNG, Phan Tri KIEN

University of Finance and Marketing, 77 Nguyen Kiem Street, Phu Nhuan District, Ho Chi Minh City, Vietnam

Received:2020-01-06 Revised:2020-09-28 Online:2021-10-25 Published:2021-10-21
Contact: Tran Loc HUNG E-mail:tlhung@ufm.edu.vn

摘要/Abstract

摘要： The main purpose of this paper is to extend the Zolotarev's problem concerning with geometric random sums to negative binomial random sums of independent identically distributed random variables. This extension is equivalent to describing all negative binomial infinitely divisible random variables and related results. Using Trotter-operator technique together with Zolotarev-distance's ideality, some upper bounds of convergence rates of normalized negative binomial random sums (in the sense of convergence in distribution) to Gamma, generalized Laplace and generalized Linnik random variables are established. The obtained results are extension and generalization of several known results related to geometric random sums.

关键词: Zolotarev's problem, geometric random sum, negative binomial random sum, negative binomial infinitely divisibility, Trotter-operator technique

Abstract: The main purpose of this paper is to extend the Zolotarev's problem concerning with geometric random sums to negative binomial random sums of independent identically distributed random variables. This extension is equivalent to describing all negative binomial infinitely divisible random variables and related results. Using Trotter-operator technique together with Zolotarev-distance's ideality, some upper bounds of convergence rates of normalized negative binomial random sums (in the sense of convergence in distribution) to Gamma, generalized Laplace and generalized Linnik random variables are established. The obtained results are extension and generalization of several known results related to geometric random sums.

Key words: Zolotarev's problem, geometric random sum, negative binomial random sum, negative binomial infinitely divisibility, Trotter-operator technique

中图分类号:

60E07

Tran Loc HUNG, Phan Tri KIEN. AN EXTENSION OF ZOLOTAREV'S PROBLEM AND SOME RELATED RESULTS[J]. 数学物理学报(英文版), 2021, 41(5): 1619-1634.

Tran Loc HUNG, Phan Tri KIEN. AN EXTENSION OF ZOLOTAREV'S PROBLEM AND SOME RELATED RESULTS[J]. Acta mathematica scientia,Series B, 2021, 41(5): 1619-1634.

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AN EXTENSION OF ZOLOTAREV'S PROBLEM AND SOME RELATED RESULTS

AN EXTENSION OF ZOLOTAREV'S PROBLEM AND SOME RELATED RESULTS

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