If $g$ is the transform of a martingale $f$ under a predictable sequence $v$ uniformly bounded in absolute value by 1, then $$\lambda P(g^\ast \geqslant \lambda) \leqslant 2\|f\|_1, \lambda > 0$$, and this inequality is sharp.
Publié le : 1979-10-14
Classification:
Martingale,
martingale transform,
maximal function,
square function,
Brownian motion,
Ito integral,
60G45,
60H05
@article{1176994944,
author = {Burkholder, D. L.},
title = {A Sharp Inequality for Martingale Transforms},
journal = {Ann. Probab.},
volume = {7},
number = {6},
year = {1979},
pages = { 858-863},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994944}
}
Burkholder, D. L. A Sharp Inequality for Martingale Transforms. Ann. Probab., Tome 7 (1979) no. 6, pp. 858-863. http://gdmltest.u-ga.fr/item/1176994944/