A MAXIMAL INEQUALITY FOR STOCHASTIC INTEGRALS

被引：0
|
作者：
Rapicki, Mateusz [1 ]
机构：
[1] Univ Warsaw, Fac Math Informat & Mech, Ul Banacha 2, PL-02097 Warsaw, Poland
来源：
PROBABILITY AND MATHEMATICAL STATISTICS-POLAND | 2016年 / 36卷 / 02期
关键词：
Martingale; sharp inequality; SHARP INEQUALITIES; FOURIER MULTIPLIERS; MARTINGALE TRANSFORMS; RIESZ TRANSFORMS;
D O I：
暂无
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：
Assume that X is a cadlag, real-valued martingale starting from zero, H is a predictable process with values in [-1; 1] and Y = integral H dX. This article contains the proofs of the following in qualities: (i) If X has continuous paths, then P(sup(t >= 0) Y-t >= 1) <= 2E sup(t-0) X-t, where the constant 2 is the best possible. (ii) If X is arbitrary, then P (sup(t) Y->= 0(t) >= 1) <= cE sup(t >= 0) X-t,X- where c = 3.0446... is the unique positive number satisfying the equation 3c(4) - 8c(3) - 32 = 0. This constant is the best possible.
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页码：311 / 333
页数：23
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