On the covering by small random intervals

被引：22

作者：

Fan, AH ^{[1
]}

Wu, J

机构：

[1] Wuhan Univ, Dept Math, Wuhan 430072, Hubei, Peoples R China

[2] Univ Picardie, CNRS, UMR 6140, LAMFA, F-80039 Amiens, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2004年 / 40卷 / 01期

关键词：

random covering; uniform sample spacing; Hausdorff dimension;

D O I：

10.1016/j.anihpb.2003.07.001

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Consider the random intervals I-n = omega(n) + (0, ln) (modulo 1) with their left points omega(n) independently and uniformly distributed over the interval [0,1) = R/Z and with their lengths decreasing to zero. We prove that the Hausdorff dimension of the set (lim) over bar I-n(n) of points covered infinitely often is almost surely equal to 1/alpha when l(n) = a/n(alpha) for some a > 0 and alpha > 1. (C) 2003 Elsevier SAS. All rights reserved.

引用

页码：125 / 131

页数：7

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