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December, 1979 A Martingale Inequality for the Square and Maximal Functions
Louis H. Y. Chen
Ann. Probab. 7(6): 1051-1055 (December, 1979). DOI: 10.1214/aop/1176994898

Abstract

An inequality for certain random sequences more general than martingales or nonnegative submartingales is proved. Three special cases are deduced, one of which generalizes and refines a result of Austin. As an application of the inequality, the special cases are used to give new proofs of Burkholder's $L \log L$ and $L_p$ (for $1 < p \leqslant 2$) inequalities for the square function of a martingale or a nonnegative submartingale.

Citation

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Louis H. Y. Chen. "A Martingale Inequality for the Square and Maximal Functions." Ann. Probab. 7 (6) 1051 - 1055, December, 1979. https://doi.org/10.1214/aop/1176994898

Information

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

zbMATH: 0421.60039
MathSciNet: MR548899
Digital Object Identifier: 10.1214/aop/1176994898

Subjects:
Primary: 60G45

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 6 • December, 1979
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