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December, 1972 An Equivalent to the Martingale Square Function Inequality
Louis Gordon
Ann. Math. Statist. 43(6): 1927-1934 (December, 1972). DOI: 10.1214/aoms/1177690863


A direct proof is given for an inequality relating the expected absolute value of stopped Brownian motion to the expected time to stopping. This inequality was originally proved by means of the martingale square function inequality. The latter is then derived from the former through use of a Skorokhod embedding. The first inequality is also applied to prove a martingale strong law of large numbers.


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Louis Gordon. "An Equivalent to the Martingale Square Function Inequality." Ann. Math. Statist. 43 (6) 1927 - 1934, December, 1972.


Published: December, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0267.60046
MathSciNet: MR386006
Digital Object Identifier: 10.1214/aoms/1177690863

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 6 • December, 1972
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