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.
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页码：1405 / 1408
页数：4
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