Sharp maximal bound for continuous martingales

被引：0

作者：

Osekowski, Adam ^{[1
]}

机构：

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

来源：

STATISTICS & PROBABILITY LETTERS | 2010年 / 80卷 / 17-18期

关键词：

Martingale; Stochastic integral; Maximal inequality; Differential subordination; STOCHASTIC INTEGRALS; INEQUALITIES; TRANSFORMS;

D O I：

10.1016/j.spl.2010.05.005

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 X, Y be continuous-path martingales satisfying the condition [X, X](t) >= [Y, Y](t) for all t >= 0. We prove that parallel to sup(t >= 0) Y(t)parallel to(1) <= 3/2 parallel to sup(t >= 0)vertical bar X(t)vertical bar parallel to(1) and the constant 3/2 is the best possible. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：1405 / 1408

页数：4

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