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随机和局部精细大偏差的应用 被引量：1

The Application for Local Precise Large Deviation Probability of Random Sums
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摘要 研究了在F∈SΔ,Δ=(0,T],T≤∞的条件下随机和S(T)=SUM from i=1 to N(t) ξi,t≥0中心化的局部精细大偏差结果中{h(t),t≥0}和{J(t),t≥0}的选取,并且给出了随机和的局部精细大偏差在索赔过程和再保险中的应用. It is discussed that how to choose {h（t）,t O} and {J（t）,t 〉t O} in the local large deviation result for the random sum S（t）= , t≥O under the condition F∈SA, where A=（O,T], T≤oo, and{N（t）,t≥O}be a Possion process independent of { ≥1}. Its applications in claim risk process and reinsurance treaties are also discussed.
作者 明瑞星 黄丽 周少南
机构地区 江西师范大学数学与信息科学学院
出处 《江西师范大学学报（自然科学版）》 CAS 北大核心 2011年第5期471-477,共7页 Journal of Jiangxi Normal University(Natural Science Edition)
基金 国家自然科学基金(43007201) 江西省自然科学基金(2008GQS0035)资助项目
关键词 局部次指数族 随机和 大偏差 复合泊松过程 local subexponentiality random sum large deviation compound poisson process
分类号 O211.4 [理学—概率论与数理统计] O211.5 [理学—概率论与数理统计]
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参考文献13

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二级参考文献6

  • 1苏淳,唐启鹤,江涛.A contribution to large deviations for heavy-tailed random sums[J].Science China Mathematics,2001,44(4):438-444. 被引量：27
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共引文献28

同被引文献13

  • 1Heyde C C. On large deviation problems for sums of ran- dom variables which are not attracted to the normal law [ J ]. Ann Math Statist, 1967,38 ( 5 ) : 1575-1578.
  • 2Heyde C C. A contribution to the theory of large deviations for sums of independent random variables [ J ]. Zeitschrift ftlr Wabrscheinlichkeitstheorie und Verwandte Gebiete, 1967,7 (5) :303-308.
  • 3Cline I) B H, Hsing T. Large deviation probabilities for sums and maxima of random variables with heavy or sub- exponential tails [ D ]. Corpus Christi : Texas A and M Uni- versity, 1991.
  • 4Khlppelberg C, Mikosch T. Large deviations of heavy-tailed random sums with applications in insurance and finance [ J ]. J Appl Prob, 1997,34 ( 2 ) : 293-308.
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  • 6Liu Li. Precise large deviations for dependent random vari- ables with heavy tails [ J ]. Stat Prob Lett, 2009,79 (9) : 1290-1298.
  • 7Ng K W, Tang Qihe, Yan Jia' an, et al. Precise large devi- ations for the prospective-loss process [ J ]. J Appl Prob- ab,2003,40(2) :391-400.
  • 8Block H W, Savits T H, Shaked M. Some concepts of nega- tive dependence [ J ]. Ann Probab, 1982,10 ( 3 ) :765-772.
  • 9Tang Qihe. Insensitivity to negative dependence of the as- ymptotic behavior of precise large deviations [ J ]. Electron Prob,2006,11 (4) :107-120.
  • 10马学敏,胡亦钧.复合二项过程风险模型的精细大偏差及有限时间破产概率[J].数学学报（中文版）,2008,51(6):1119-1130. 被引量：7

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江西师范大学学报（自然科学版）
2011年 第5期

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