NEW PROOFS OF KHINCHIN'S LAW OF LARGE NUMBERS AND LINDEBERG'S CENTRAL LIMIT THEOREM -PDE'S APPROACH

被引：0

作者：

Meng, Xue ^{[1
]}

Gao, Miaomiao ^{[2
]}

Hu, Feng ^{[1
]}

机构：

[1] Qufu Normal Univ, Sch Stat & Data Sci, Qufu 273165, Shandong, Peoples R China

[2] Jining Univ, Dept Math, Qufu 273199, Shandong, Peoples R China

来源：

MATHEMATICAL FOUNDATIONS OF COMPUTING | 2023年 / 6卷 / 02期

基金：

美国国家科学基金会;

关键词：

Khinchin's LLN; Lindeberg's CLT; PDE;

D O I：

10.3934/mfc.2022017

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Both Khinchin's law of large numbers (Khinchin's LLN) and Lindeberg's central limit theorem (Lindeberg's CLT) are fundamental results in probability theory. In this paper, we give the new proofs of these two theorems. A law of large numbers and a central limit theorem are proved for independent and non-identical distributed random variables. Indeed, these results include the Khinchin's LLN and Lindeberg's CLT. Our main tool is the viscosity solution theory of partial differential equation (PDE).

引用

页码：190 / 202

页数：13

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