On Large Deviations of a Sum of Independent Random Variables with Rapidly Decreasing Distribution Tails

被引：1

作者：

Rozovsky, L., V ^{[1
]}

机构：

[1] St Petersburg State Chem & Pharmaceut Univ, St Petersburg, Russia

来源：

DOKLADY MATHEMATICS | 2020年 / 101卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

independent random variables; large deviations; rapidly decreasing tails; CONVOLUTION EQUIVALENCE; ASYMPTOTICS;

D O I：

10.1134/S1064562420020210

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a sum of a finite number of independent random variables, the asymptotic behavior of its distributions and densities at infinity is investigated in the case when the densities or tails of these distributions decrease faster than the densities or tails of gamma distributions.

引用

页码：150 / 153

页数：4

共 8 条

[1]

Borovkov A., 2008, ASYMPTOTIC ANAL RAND

[2]

CLINE DBH, 1986, PROBAB THEORY REL, V72, P529, DOI 10.1007/BF00344720

[3] On the exact asymptotics for the stationary sojourn time distribution in a tandem of queues with light-tailed service times [J].

Foss, S. G. .

PROBLEMS OF INFORMATION TRANSMISSION, 2007, 43 (04) :353-366

[4] LARGE DEVIATIONS OF SUMS OF INDEPENDENT RANDOM-VARIABLES [J].

NAGAEV, SV .

ANNALS OF PROBABILITY, 1979, 7 (05) :745-789

[5] Convolution equivalence and infinite divisibility [J].

Pakes, AG .

JOURNAL OF APPLIED PROBABILITY, 2004, 41 (02) :407-424

[6] Superlarge deviations of a sum of independent random variables having a common absolutely continuous distribution under the Cramer condition [J].

Rozovsky, LV .

THEORY OF PROBABILITY AND ITS APPLICATIONS, 2003, 48 (01) :108-130

[7] Convolution equivalence and distributions of random sums [J].

Watanabe, Toshiro .

PROBABILITY THEORY AND RELATED FIELDS, 2008, 142 (3-4) :367-397

[8] On the exact distributional asymptotics for the supremum of a random walk with increments in a class of light-tailed distributions [J].

Zachary, S. ;

Foss, S. G. .

SIBERIAN MATHEMATICAL JOURNAL, 2006, 47 (06) :1034-1041

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