On the best constant in the weak type inequality for the square function of a conditionally symmetric martingale

被引：6

作者：

Osekowski, Adam ^{[1
]}

机构：

[1] Univ Warsaw, Dept Math Informat & Mech, PL-02097 Warsaw, Poland

来源：

STATISTICS & PROBABILITY LETTERS | 2009年 / 79卷 / 13期

关键词：

D O I：

10.1016/j.spl.2009.03.017

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：

Let f be a real conditionally symmetric martingale and S(f) denote its square function. The purpose of this note is to show that the inequality sup(lambda > 0)(lambda P(S(f) >= lambda)) <= K parallel to f parallel to(1). K = exp(-1/2) + integral(1)(0) exp(-t(2)/2)dt approximate to 1,4622 due to Bollobas, is sharp. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：1536 / 1538

页数：3