On a Weak Law of Large Numbers with Regularly Varying Normalizing Sequences

被引：10

作者：

Boukhari, Fakhreddine ^{[1
]}

机构：

[1] Univ Abou Bekr Belkaid Tlemcen, Lab Stat & Modelisat Aleatoires, Fac Sci, BP 119, Tilimsen 13000, Algeria

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2022年 / 35卷 / 03期

关键词：

Kolmogorov-Feller weak law; General limit theorems; Pairwise NQD random variables; Slow variation; RANDOM-VARIABLES; KOLMOGOROV; EXTENSION; SUMS;

D O I：

10.1007/s10959-021-01120-6

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The Kolmogorov-Feller weak law of large numbers for i.i.d. random variables has been extended by Gut (J. Theoret. Probab. 17, 769-779, 2004) to the case where the normalizing sequence is regularly varying with index 1/rho for some rho is an element of]0, 1]. In this paper, we showthat the sufficiency part inGut's theorem is valid without any restriction on the dependence structure of the underlying sequence, provided that rho not equal 1. We also prove the necessity part in Gut's weak law of large numbers when the summands are pairwise negatively dependent.

引用

页码：2068 / 2079

页数：12

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