记录时及其计数过程精确渐近性的一般形式  

General Form of Precise Asymptotics for Record Times and Its Counting Process

作　　者：李玉玲[1] 赵辉艳 LI Yuling;ZHAO Huiyan(Research Center for Applied Mathematics and Interdisciplinary Sciences,Beijing Normal University at Zhuhai,Zhuhai 519087,Guangdong Province,China)

机构地区：[1]北京师范大学珠海校区应用数学与交叉科学研究中心,广东珠海519087

出　　处：《吉林大学学报（理学版）》2023年第2期285-291,共7页Journal of Jilin University:Science Edition

基　　金：广东省普通高校特色创新项目(批准号:201912009QX).

摘　　要：设{X_(n),n≥1}是独立同分布的连续型随机变量,记录时刻序列为{L_(n),n≥1},对应的计数过程为{μn,n≥1}.利用记录时及其计数过程的中心极限定理、矩不等式和Berry-Esseen不等式,给出边界函数和拟权函数记录时及相应计数过程的精确渐近性的一般结果.Let{X_(n),n≥1}be an independent and identically distributed continuous random variables,let{L_(n),n≥1}and{μn,n≥1}be the record times sequence and corresponding counting process.By using the central limit theorem,the moment inequalities and the Berry-Esseen inequalities of the record times and its counting process,a general result of precise asymptotics for the record times and corresponding counting process were obtained for the boundary function and quasi-weight function.

关 键 词：计数过程 记录时 精确渐近性 一般形式 

分 类 号：O211.4[理学—概率论与数理统计]