Asymptotics of random sums of negatively dependent random variables in the presence of dominatedly varying tails

被引：5

作者：

Yang, Yang ^{[1
,2
]}

Leipus, Remigijus ^{[3
,4
]}

Siaulys, Jonas ^{[3
]}

机构：

[1] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

[2] Nanjing Audit Univ, Sch Math & Stat, Nanjing 210029, Jiangsu, Peoples R China

[3] Vilnius Univ, Fac Math & Informat, LT-03225 Vilnius, Lithuania

[4] Vilnius Univ, Inst Math & Informat, LT-08663 Vilnius, Lithuania

来源：

LITHUANIAN MATHEMATICAL JOURNAL | 2012年 / 52卷 / 02期

基金：

美国国家科学基金会; 中国博士后科学基金;

关键词：

negative dependence; dominated variation; random sums; dependent compound renewal risk model; PRECISE LARGE DEVIATIONS; HEAVY TAILS; DISTRIBUTIONS; BEHAVIOR;

D O I：

10.1007/s10986-012-9169-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (1) (2) be a sequence of negatively dependent and identically distributed random variables, and let be a counting random variable independent of 's. In this paper, we study the asymptotics for the tail probability of the random sum S-N = Sigma(N)(k=1) in the presence of heavy tails. We consider the following three cases: (i) () = (( (1) )), and the distribution function (d.f.) of (1) is dominatedly varying; (ii) ( (1) ) = (()), and the d.f. of is dominatedly varying; (iii) the tails of (1) and are asymptotically comparable and dominatedly varying.

引用

页码：222 / 232

页数：11

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