A lower bound for the tail probability of partial maxima of dependent random variables and applications

被引：6

作者：

Boukhari, Fakhreddine ^{[1
]}

机构：

[1] Abou Bekr Belkaid Univ, Fac Sci, Dept Math, BP 119, Tilimsen 13000, Algeria

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2021年 / 131卷 / 01期

关键词：

AANA sequences; Kolmogorov– Feller weak law; complete convergence; Baum– Katz strong law; limit theorems;

D O I：

10.1007/s12044-021-00607-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish a non-asymptotic lower bound for the running maximum of an asymptotically almost negatively associated (AANA) family of random variables. The obtained result is applied to characterize the Kolmogorov-Feller weak law of large numbers for these sequences. We also provide a simplified proof of the necessity part in the Baum-Katz law of large numbers in the AANA setting.

引用

页数：13

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