| 独立重尾随机变量随机和的大偏差估计 |
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| 引用本文： | 李克文,胡亦钧. 独立重尾随机变量随机和的大偏差估计[J]. 数学杂志, 2002, 22(2): 131-139 |
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| 作者姓名： | 李克文 胡亦钧 |
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| 作者单位： | 武汉大学数学与统计学院,武汉,430072 |
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| 基金项目： | theNationalNaturalScienceFoundationofChinaandtheDepartmentofEducationofChina |
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| 摘 要： | 本文研究了一类独立重尾随机变量随机和S（t)∧=∑k=1^N(t)Xk,t≥0的大偏差概率，其中{N(t),t≥0}是一放大晨负整数值随机变量；{Xn,n≥1}是非负，独立随机变量序列，并与{N(t),t≥０}独立。本文的结果将{Xn,n≥１}为独立同分布情形推广到了独立不同分布情形。
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| 关 键 词： | 独立重尾随机变量 随机和 大偏差估计 正则变化 扩展正则变化 精确大偏差 |
AN ESTIMATE OF LARGE DEVIATIONS FOR HEAVY-TAILED RANDOM SUMS OF INDEPENDENT RANDOM VARIABLES |
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| LI Kewen,Hu Yijun. AN ESTIMATE OF LARGE DEVIATIONS FOR HEAVY-TAILED RANDOM SUMS OF INDEPENDENT RANDOM VARIABLES[J]. Journal of Mathematics, 2002, 22(2): 131-139 |
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| Authors: | LI Kewen Hu Yijun |
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| Abstract: | In this paper, we investigate the precise large deviation for heavy-tailed random sums S(t) N(t) ∑Xk , for t ≥0, where {N(t),t ≥ 0} are non-negative integer-valued random variables, and k=1{Xn, n ≥ 1} , independentof{N(t),t≥0} , are non-negative, independent random variables. Our re-sults extend the classical results under the case that Xn, n ≥ 1 } are independent and identically distributed by extended regular variation. |
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| Keywords: | regular variation extended regular variation precise large deviation large deviation |
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