NA随机变量随机和的差的精确大偏差  

Precise Large Deviation for the Difference of Random Sum of NA Random Variables

作　　者：华志强[1] 张春生[1] 陈丽莹[1] 盛婷婷[1] HUA Zhiqiang;ZHANG Chunsheng;CHEN Liying;SHENG Tingting(College of Mathematics,Inner Mongolia University for the Nationalities,Tongliao Inner Mongolia 028043,China)

机构地区：[1]内蒙古民族大学数学学院,内蒙古通辽028043

出　　处：《重庆师范大学学报（自然科学版）》2018年第5期88-93,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.81460656;No.61663037);内蒙古自治区自然科学基金(No.2017MS(LH)0106;No.2018MS06016);内蒙古民族大学科学研究基金(No.NMDGP17105)

摘　　要：【目的】研究由两类保单构成的随机和的差N1(t)∑j=1X1j-N2(t)∑j=1X2j的相依风险模型,该风险模型中第一类保单{X1j,j≥1}是一个负相协(Nagatively associated,NA)随机变量序列,{X2j,j≥1}是一个独立的随机变量序列,{N1(t),t≥0}和{N2(t),t≥0}是两个计数过程。【方法】采用类似求独立随机变量随机和的差的精确大偏差的渐近极限方法,研究了NA随机变量随机和的差的精确大偏差问题。【结果】引入一些假设条件,得到如下的一致渐近极限结论,即:对于任意固定的γ>μ2,有limt→∞supx≥γ(λ1(t))p+1|P(N1(t)∑j=1X1j-N2(t)∑j=1X2j-(μ1λ1(t)-μ2λ2(t))>x)/λ1(t)F1(x)-1|=0。【结论】推广了独立随机变量随机和的差的精确大偏差的相应结论。[Purposes]It investigates the dependent risk model of the random difference N1（t）∑j=1X1j-N2（t）∑j=1X2j between the two types ofpolices,where{X1 j,j≥1}is a sequence of NA（negatively associated）random variables,{X2 j,j≥1}is a sequence of independent random variables,{N1（t）,t≥0}and{N2（t）,t≥0}are two independent counting processes.[Methods]Study the issue of precise large deviation for the difference of random sum of NArandom variables by using the similar method to find the asymptotic limit of the precise large deviation for the difference of random sum of independent random variables.[Findings]Under some given assumptions, the following uniformly asymptotic limit is established, that is, for any fixed γ 〉μ2,limt→∞supx≥γ（λ1（t））p＋1｜P（N1（t）∑j=1X1j-N2（t）∑j=1X2j-（μ1λ1（t）-μ2λ2（t））〉x）/λ1（t）F1（x）-1｜=0.[Conclusions]This result generalizes the corresponding result of the precise large deviation for the difference of random sum of independent random variables.

关 键 词：精确大偏差 负相协 随机和的差 

分 类 号：O211.4[理学—概率论与数理统计]