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 tail

作　　者：冯敬海[1] 宋立新[1] 包莹莹[1] 

机构地区：[1]大连理工大学数学科学学院,辽宁大连116024

出　　处：《大连理工大学学报》2014年第4期482-486,共5页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(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)

摘　　要：基于带O正则变化独立同分布随机变量的部分和的局部精确大偏差的相关结论,将其对应的随机和分为3个部分,利用次指数函数的相互关系以及控制收敛定理,分别证明每个部分的渐近性.最后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性.Based on the local precise large deviations for non-random sum results of random variables with O-regularly varying densities,the random sums of independent identical distribution random variables are divided into three parts and the asymptotic behavior of each part is proved by the relationship of subexponential functions and control convergence theorem.Finally,the asymptotic behavior of local precise large deviations for random sums with consistently varying tail is proved.

关 键 词：局部精确大偏差 渐近性 一致变化尾 随机和 

分 类 号：O211[理学—概率论与数理统计]