| 纪录时刻及其计数过程矩完全收敛的精确渐近性 |
| |
| 引用本文： | 沈炎峰.纪录时刻及其计数过程矩完全收敛的精确渐近性[J].浙江大学学报(理学版),2010,37(1):12-16. |
| |
| 作者姓名： | 沈炎峰 |
| |
| 作者单位： | 浙江大学,数学系,浙江,杭州,310027 |
| |
| 摘 要： | 设{Xn,n≥1}是i.i.d.连续型随机变量,μ(n)为记录时刻对应的计数过程,记N为服从标准正态分布的随机变量,证明了μ(n)矩完全收敛的精确渐近性,即当1p2,δ-1时,有limε10ε2p(δ+1)/(2-p)∑n≥3(logn)δ/n(logn)-1/2E{|μ(n)-logn|-ε(logn)1/p}+=1/δ+1·2-p/2pδ+p+2E|N|(2pδ+p+2)/(2-p).
|
| 关 键 词： | 精确渐近性 记录时刻 计数过程 |
Precise asymptotics in the complete moment convergence of record times and the associated counting process |
| |
| SHEN Yan-feng.Precise asymptotics in the complete moment convergence of record times and the associated counting process[J].Journal of Zhejiang University(Sciences Edition),2010,37(1):12-16. |
| |
| Authors: | SHEN Yan-feng |
| |
| Institution: | SHEN Yan-feng(Department of Mathematics, Zhejiang University, Hangzhou 310027, China) |
| |
| Abstract: | Let{X_n,n≥1} be i.i.d. Continuous random variables and μ(n) be the associated counting process of record times,the following result is proved: limε↘0 ε～(2p(δ+1)/(2-p))∑n≥3((log n)～δ)/(n)(log n)～(-1/2)E{|μ(n)-log n|-ε(log n)～(1/p)}_+=(1)/(δ+1)·(2-p)/(2pδ+p+2)E|N|～((2pδ+p+2)/(2-p)),whenever 1-1. |
| |
| Keywords: | precise asymptotics record times counting process |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
| 点击此处可从《浙江大学学报(理学版)》浏览原始摘要信息 |
| 点击此处可从《浙江大学学报(理学版)》下载免费的PDF全文 |
|
