A general large deviation result for partial sums of i.i.d. super-heavy tailed random variables

被引：2

作者：

Li, Deli ^{[1
]}

Miao, Yu ^{[2
]}

Stoica, George ^{[3
]}

机构：

[1] Lakehead Univ, Dept Math Sci, Thunder Bay, ON, Canada

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

[3] Univ New Brunswick, Dept Math & Stat, Fredericton, NB, Canada

来源：

STATISTICS & PROBABILITY LETTERS | 2022年 / 184卷

基金：

中国国家自然科学基金; 加拿大自然科学与工程研究理事会;

关键词：

Large deviations; Sums of i; i; d; random variables; Super-heavy tailed random variables; LIMIT-THEOREMS;

D O I：

10.1016/j.spl.2022.109371

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：

In this paper, a general large deviation result for partial sums of independent and identically distributed random variables with super-heavy tailed distribution is established. Our main result extends in particular the results of Stoica (2008) and Nakata (2022). The symmetrization technique, one of Levy's inequalities, and two preliminary results on slowly and regularly varying functions are paramount in the proof of our main result.(c) 2022 Elsevier B.V. All rights reserved.

引用

页数：10

共 19 条

[11] Large deviations for heavy-tailed random sums of independent random variables with dominatedly varying tails
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[12] Large deviations for heavy-tailed random sums of independent random variables with dominatedly varying tails
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Hu, YJ
SCIENCE IN CHINA SERIES A-MATHEMATICS, 2003, 46 (03): : 383 - 395
[13] Large deviations for heavy-tailed random sums of independent random variables with dominatedly varying tails
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[14] Super large deviation probabilities for sums of independent lattice random variables with exponential decreasing tails
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[17] Uniform Estimates for Distributions of the Sum of i.i.d. Random Variables with Fat Tail in the Threshold Case
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[18] Complete and complete moment convergence for i.i.d. random variables under exponential moment conditions
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[19] ON CSRG■-RVSZ'S INCREMENTS OF SUMS OF NON-I. I. D. RANDOM VARIABLES
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