Small Deviations of the Maximal Element of a Sequence of Weighted Independent Random Variables

被引：0
|
作者：
Rozovskii, L. V. [1 ]
机构：
[1] St Petersburg Inst Chem & Pharmacol, Ul Prof Popova 14, St Petersburg 197376, Russia
来源：
VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS | 2011年 / 44卷 / 02期
基金：
俄罗斯基础研究基金会;
关键词：
small deviations; maximal element; nonnegative random variables; slowly varying functions; regularly varying functions;
D O I：
10.3103/S1063454111020117
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Consider a sequence {X-i} of independent copies of a nonnegative random variable X and let M = sup(j) (>=) (1)lambda X-j(j), where {lambda(j)} is a nonincreasing sequence of positive numbers for which P(M < infinity) = 1. The asymptotic behavior of -logP(M < r) as r -> 0 is studied. A similar problem has been considered for weights {lambda(j)} of special form. This paper studies the fairly important and general case in which -logP(M< r) has an explicit asymptotics as r -> 0.
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页码：129 / 133
页数：5
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