LARGE DEVIATIONS FOR SOME DEPENDENT HEAVY TAILED RANDOM SEQUENCES

被引：0

作者：

Yin, Qing ^{[1
]}

Miao, Yu ^{[1
,2
]}

机构：

[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China

[2] Henan Normal Univ, Henan Engn Lab Big Data Stat Anal & Optimal Contr, Xinxiang 453007, Henan, Peoples R China

来源：

MATHEMATICA SLOVACA | 2024年 / 74卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Large deviations; heavy tailed; acceptable random variables; widely acceptable random variables; RANDOM-VARIABLES; CONVERGENCE;

D O I：

10.1515/ms-2024-0017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, let {X-n, n >= 1} be a sequence of random variables with heavy tailed distributions and define S-n = X-1 + X-2 + center dot center dot center dot + X-n, max(1 <= k <= n) S-k = max{S-1, S-2, . . . , S-n} and M-n = max{X-1, X-2, . . . , X-n}. We consider the large deviation behaviors and establish the upper bounds of large deviations for the above three quantities based on some dependent random variables {X-n, n >= 1}, such as acceptable random variables, widely acceptable random variables and a class of random variables that satisfies the Marcinkiewicz-Zygmund type inequality and Rosenthal type inequality. Furthermore, the lower bounds of large deviations for some non-negative and identically distributed dependent sequences are obtained. (c) 2024 Mathematical Institute Slovak Academy of Sciences

引用

页码：221 / 234

页数：14

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