具有随机足标的强相依正态序列部分和与最大值的联合极限分布  

On the Joint Limiting Distribution of the Partial Sum and Maximum of Strongly Dependent Stationary Normal Sequence with Random Index

作　　者：胡爱平[1] 伍度志[2] 

机构地区：[1]西南师范大学数学系,重庆400715 [2]后勤工程学院基础部,重庆400016

出　　处：《西南师范大学学报（自然科学版）》2003年第4期529-532,共4页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：设X1,X2,…是标准化的平稳正态序列.Mn=max1≤i≤nXi,ρn=EX1Xn+1,Sn=∑ni=1Xi,{N(n)}是一列取非负整值的随机变量,且N(n)nPη>0,η为随机变量.在ρn和(ρn·logn)-1都单调趋于0的条件下,得到了MN(n)和SN(n)的联合极限分布.Let X1, X2, ...be a stationary sequence of normal random variables with common distribution, and Mn=max{Xi|1≤i≤n}, ρn=EX1Xn+1, Sn=∑ni=1Xi. Suppose {N(n)} is a nonnegative integer valued random variable with N(n)nPη>0, as n∞ for a given random variable η. When ρn and (ρn log n)-1 both are convergence to 0, the joint limiting distribution of MN(n) and SN(n) is derived. 

关 键 词：强相依正态序列 随机足标 部分和 最大值 联合极限分布 随机变量序列 正态分布 

分 类 号：O211.3[理学—概率论与数理统计]