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机构地区:[1]太原工业学院理学系,太原030008 [2]大连理工大学数学科学学院,大连116024
出 处:《应用概率统计》2016年第4期393-407,共15页Chinese Journal of Applied Probability and Statistics
基 金:supported by the National Natural Sciences Foundation of China(11101061,11371077 and61175041)
摘 要:本文研究非负,不同分布,负相协随机变量的精细大偏差问题.在相对较弱的条件下,重点解决了非随机和的精细大偏差的下限问题,得到相对应的随机和的一致渐近结论.同时,对复合更新风险模型进行了深入的讨论,在一定的条件之下将其简化为一般的更新模型,并将所得相关的精细大偏差的结论应用到更为实际的复合更新风险模型中,验证了其理论与实际价值.除此之外,本文的研究还表明,随机变量间的这种相依关系对精细大偏差的最终结果的影响并不大.In this paper, precise large deviations of nonnegative, non-identical distributionsand negatively associated random variables are investigated. Under certain conditions, the lower bound of the precise large deviations for the non-random sum is solved and the uniformly asymptotic results for the corresponding random sum are obtained. At the same time, we deeply discussed the compound renewal risk model, in which we found that the compound renewal risk model can be equivalent to renewal risk model under certain conditions. The relative research results of precise large deviations are applied to the more practical compound renewal risk model, and the theoretical and practical values are verified. In addition, this paper also shows that the impact of this dependency relationship between random variables to precise large deviations of the final result is not significant.
关 键 词:精细大偏差 负相协 非随机和 随机和 复合更新风险模型
分 类 号:O211.4[理学—概率论与数理统计]
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