A supplement to the large deviations of infinite weighted sums of heavy tailed random variables

被引：0

作者：

Shi, Jianan ^{[1
]}

Yu, Zhenhong ^{[1
]}

Miao, Yu ^{[1
,2
]}

机构：

[1] Henan Normal Univ, Sch Math & Stat, Xinxiang 453007, Henan Province, Peoples R China

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

来源：

STATISTICS & PROBABILITY LETTERS | 2025年 / 217卷

基金：

中国国家自然科学基金;

关键词：

Independent identically distributed random; variables; Large deviations; Heavy tails; Weighted sums;

D O I：

10.1016/j.spl.2024.110306

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：

Let { X , Xn, n >= 1} be a sequence of independent and identically distributed non-negative random variables with heavy tails and { a i ( n ) , i >= 1 , n >= 1} be an array of non-negative numbers. In the present paper, we study the large deviation of infinite weighted sums & sum; infinity i =1 ai(n)Xi, which is a supplement of Aurzada (2020).

引用

页数：8

共 13 条

[1] Large deviations for infinite weighted sums of stretched exponential random variables [J].

Aurzada, Frank .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 485 (02)

[2]

Bonin O., 2003, Probab. Math. Statist., V23, P357

[3] LARGE DEVIATION THEOREM FOR WEIGHTED SUMS [J].

BOOK, SA .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1973, 26 (01) :43-49

[4] LARGE DEVIATION PROBABILITIES FOR WEIGHTED SUMS [J].

BOOK, SA .

ANNALS OF MATHEMATICAL STATISTICS, 1972, 43 (04) :1221-&

[5] Asymptotic expansion of the distribution density function for the sum of random variables in the series scheme in large deviation zones [J].

Deltuviene, D ;

Saulis, L .

ACTA APPLICANDAE MATHEMATICAE, 2003, 78 (1-3) :87-97

[6]

Dembo A., 1998, Large Deviations Techniques and Applications, DOI DOI 10.1007/978-1-4612-5320-4

[7] Large deviations for weighted sums of stretched exponential random variables [J].

Gantert, Nina ;

Ramanan, Kavita ;

Rembart, Franz .

ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2014, 19 :1-14

[8]

Giuliano R, 2012, ANN MATH INFORM, V39, P109

[9] Large deviation principles for sequences of logarithmically weighted means [J].

Giuliano, Rita ;

Macci, Claudio .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 378 (02) :555-570

[10] A large deviation principle for weighted sums of independent identically distributed random variables [J].

Kiesel, R ;

Stadtmüller, U .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 251 (02) :929-939

← 1 2 →