| Moderate Deviations for Random Sums of Heavy-Tailed Random Variables |
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| 引用本文： | Fu Qing GAO. Moderate Deviations for Random Sums of Heavy-Tailed Random Variables[J]. 数学学报(英文版), 2007, 23(8): 1527-1536. DOI: 10.1007/s10114-007-0941-9 |
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| 作者姓名： | Fu Qing GAO |
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| 作者单位： | School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China |
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| 基金项目： | Research supported by NsFC （No. 10271091, 10571139） The author thanks Professor Cline for his preprint Cline and Hsing [9] and thanks the anonymous referee for his suggestions and comments. |
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| 摘 要： | Let {Xn;n≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E（X1） and let {N（t）; t ≥0} be a random process taking non-negative integer values with finite mean λ（t） = E（N（t）） and independent of {Xn; n ≥1}. In this paper, asymptotic expressions of P（（X1 ＋… ＋XN（t）） -λ（t）μ 〉 x） uniformly for x ∈[γb（t）, ∞） are obtained, where γ〉 0 and b（t） can be taken to be a positive function with limt→∞ b（t）/λ（t） = 0.
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| 关 键 词： | 大偏差 泊松过程 随机变量 分布函数 |
| 收稿时间： | 2003-12-29 |
| 修稿时间： | 2003-12-29 |
Moderate Deviations for Random Sums of Heavy-Tailed Random Variables |
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| Fu Qing Gao. Moderate Deviations for Random Sums of Heavy-Tailed Random Variables[J]. Acta Mathematica Sinica(English Series), 2007, 23(8): 1527-1536. DOI: 10.1007/s10114-007-0941-9 |
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| Authors: | Fu Qing Gao |
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| Affiliation: | (1) School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P. R. China |
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| Abstract: | Let {X n ; n ≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E(X 1) and let {N(t); t ≥ 0} be a random process taking non-negative integer values with finite mean λ(t) = E(N(t)) and independent of {X n ; n ≥ 1}. In this paper, asymptotic expressions of P((X 1+⋯+X N(t))−λ(t)μ > x) uniformly for x ∈ [γb(t),∞) are obtained, where γ > 0 and b(t) can be taken to be a positive function with lim t →∞ b(t)/λ(t) = 0. Research supported by NSFC (No. 10271091, 10571139) |
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| Keywords: | large deviations moderate deviations extended regular variation Poisson process |
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