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| 一致变化尾的随机和局部精确大偏差 |
| Local precise large deviations for random sums with consistently varying densities |
| 投稿时间：2013-06-16 修订日期：2013-12-18 |
| DOI： |
| 中文关键词: 局部精确大偏差 渐近性 一致变化尾 随机和 |
| 英文关键词: Local Precise large deviations Asymptotic Behavior Consistently varying density Random sums |
| 基金项目:国家自然科学基金(61175041; 11101061); 大连理工大学前沿交叉学科基金资助项目(DUT10JS06); 高等学校博士学科点专项科研基金资助项目(2010041110036) |
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| 中文摘要: |
| 随着对精确大偏差的深入研究, 以及其在保险领域中的应用, 越来越多的学者开始研究这个问题. 比如随机变量部分和大偏差和随机和的大偏差的渐近估计, 甚至多维风险模型的大偏差的极限理论以及一些相关领域的内容. 最近, 许多研究开始投向局部精确大偏差理论, 比如, 单边大偏差的局部极限定理以及随机变量和的局部概率等, 但是大多数的研究仍是以全局情况为主的, 关于局部精确大偏差的论述却不是十分完善, 尤其是在随机和局部大偏差上. 因此, 本文基于部分和局部精确大偏差的相关结论给出其拓展, 即证明了在随机变量的密度函数是一致变化尾时, 其随机和的局部精确大偏差的渐近估计. |
| 英文摘要: |
| With further study of the precise large deviations and their applications in the ?eld of insurance, more and more researchers are engaged in this topic. For example, the large deviations for nonrandom sums and random sums in the single risk model or in the multi-risk models. Recently, many results began to local precise large deviations theory, for example, local limits theorem for one-sided large precise deviations and the local probabilities for random sums. However, most studies are based on the global large deviations. The research about local precise large deviations is not very perfect, especially about local precise large deviations for random sums. So, we will give them in this paper, i.e. asymptotic behavior of local precise large deviations for random sums, which is based on the non-random sums results of them. |
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