A law of the iterated logarithm for the number of occupied boxes in the Bernoulli sieve

被引：5

作者：

Iksanov, Alexander ^{[1
]}

Jedidi, Wissem ^{[2
,3
]}

Bouzeffour, Fethi ^{[4
]}

机构：

[1] Taras Shevchenko Natl Univ Kyiv, Fac Comp Sci & Cybernet, UA-01601 Kiev, Ukraine

[2] King Saud Univ, Dept Stat & OR, POB 2455, Riyadh 11451, Saudi Arabia

[3] Univ Tunis El Manar, Fac Sci Tunis, Lab Analyse Math & Applicat LR11ES11, Tunis 2092, Tunisia

[4] King Saud Univ, Dept Math, Coll Sci, Riyadh 11451, Saudi Arabia

来源：

STATISTICS & PROBABILITY LETTERS | 2017年 / 126卷

关键词：

Bernoulli sieve; Infinite occupancy; Law of iterated logarithm; Perturbed random walk; Renewal theory;

D O I：

10.1016/j.spl.2017.03.017

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：

The Bernoulli sieve is an infinite occupancy scheme obtained by allocating the points of a uniform [0, 1] sample over an infinite collection of intervals made up by successive positions of a multiplicative random walk independent of the uniform sample. We prove a law of the iterated logarithm for the number of non-empty (occupied) intervals as the size of the uniform sample becomes large. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：244 / 252

页数：9

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