当前位置: X-MOL 学术Acta Math. Sci. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
An Extension of Zolotarev’s Problem and Some Related Results
Acta Mathematica Scientia ( IF 1 ) Pub Date : 2021-06-29 , DOI: 10.1007/s10473-021-0513-6
Tran Loc Hung , Phan Tri Kien

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.



中文翻译:

佐洛塔列夫问题的扩展和一些相关结果

本文的主要目的是将有关几何随机和的 Zolotarev 问题扩展到独立同分布随机变量的负二项式随机和。这个扩展相当于描述了所有负二项式无限可分随机变量和相关结果。使用 Trotter-operator 技术和 Zolotarev-distance 的理想性,建立了归一化负二项式随机和(在分布收敛的意义上)到 Gamma、广义拉普拉斯和广义林尼克随机变量的收敛速度的一些上限。得到的结果是对与几何随机和相关的几个已知结果的扩展和概括。

更新日期:2021-06-30
down
wechat
bug