A supplement to the laws of large numbers and the large deviations

被引：6

作者：

Li, Deli ^{[1
]}

Miao, Yu ^{[2
]}

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

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2021年 / 93卷 / 08期

基金：

加拿大自然科学与工程研究理事会; 中国国家自然科学基金;

关键词：

Laws of large numbers; large deviations; heavy-tailed random variables; logarithmic asymptotic behaviours; sums of i.i.d. random variables; SUMS; INEQUALITY;

D O I：

10.1080/17442508.2021.1903465

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let 0 < p < 2. Let {X, X-n; n >= 1} be a sequence of independent and identically distributed B-valued random variables and set S-n = Sigma(n)(i=1) X-i, n >= 1. In this paper, an analogue of large deviation principle is established under assumption S-n/n(1/p) -> P 0 only. The main tools employed in proving this result are the symmetrization technique and three powerful inequalities established by Hoffmann-Jorgensen [Sums of independent Banach space valued random variables, Studia Math. 52 (1974), pp. 159-186], de Acosta [Inequalities for B-valued random vectors with applications to the law of large numbers, Ann. Probab. 9 (1981), pp. 157-161] and Ledoux and Talagrand [Probability in Banach Spaces: Isoperimetry and Processes, Springer-Verlag, Berlin, 1991], respectively. As a special case of this result, the main results of Hu and Nyrhinen [Large deviations view points for heavy-tailedrandomwalks, J. Theoret. Probab. 17 (2004), pp. 761-768] are not only improved, but also extended.

引用

页码：1261 / 1280

页数：20

共 24 条

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