AN EXTENSION OF ZOLOTAREV'S PROBLEM AND SOME RELATED RESULTS  

作　　者：Tran Loc HUNG Phan Tri KIEN 

机构地区：[1]University of Finance and Marketing,77 Nguyen Kiem Street,Phu Nhuan District,Ho Chi Minh City,Vietnam

出　　处：《Acta Mathematica Scientia》2021年第5期1619-1634,共16页数学物理学报（B辑英文版）

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 

分 类 号：O211.5[理学—概率论与数理统计]