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October, 1979 A Sharp Inequality for Martingale Transforms
D. L. Burkholder
Ann. Probab. 7(5): 858-863 (October, 1979). DOI: 10.1214/aop/1176994944

Abstract

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.

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D. L. Burkholder. "A Sharp Inequality for Martingale Transforms." Ann. Probab. 7 (5) 858 - 863, October, 1979. https://doi.org/10.1214/aop/1176994944

Information

Published: October, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0416.60047
MathSciNet: MR542135
Digital Object Identifier: 10.1214/aop/1176994944

Subjects:
Primary: 60G45
Secondary: 60H05

Keywords: Brownian motion , Ito integral , martingale , martingale transform , maximal function , square function

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 5 • October, 1979
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