| Large deviations for heavy-tailed random sums of independent random variables with dominatedly varying tails |
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| 作者姓名： | 刘艳 胡亦钧 |
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| 作者单位： | School of Mathematics and Statistics，Wuhan University，School of Mathematics and Statistics，Wuhan University Wuhan 430072，China，Wuhan 430072，China |
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| 基金项目： | This work was supported in part by the National Natural Science Foundation of China(Grant Nos.10071058,70273209)，the Ministry of Education of China.The authors are grateful to the referees for their comments and suggestions,which led to the present imp |
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| 摘 要： | We prove large deviation results on the partial and random sums Sn = ∑i=1n Xi,n≥1; S(t) = ∑i=1N(t) Xi, t≥0, where {N(t);t≥0} are non-negative integer-valued random variables and {Xn;n≥1} are independent non-negative random variables with distribution, Fn, of Xn, independent of {N(t); t≥0}. Special attention is paid to the distribution of dominated variation.
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| 收稿时间： | 19 August 2002 |
Large deviations for heavy-tailed random sums of independent random variables with dominatedly varying tails |
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| Yan?LiuEmail author,Yijun?Hu.Large deviations for heavy-tailed random sums of independent random variables with dominatedly varying tails[J].Science in China(Mathematics),2003,46(3):383-395. |
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| Authors: | Email author" target="_blank">Yan?LiuEmail author Yijun?Hu |
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| Institution: | School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
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| Abstract: | We prove large deviation results on the partial and random sums s
n
=Σ
i=1
n
X
i
, n⩾1; S(t)=Σ
i=1
N(t)
X
i
, t⩾0, where {N(t);t⩾0} are non-negative integer-valued random variables and {X
n
;n⩾1} are independent non-negative random variables with distribution, F
n
, of X
n
, independent of {N(t);t⩾0}. Special attention is paid to the distribution of dominated variation. |
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| Keywords: | large deviations (extended) regular variation dominated variation |
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