Abstract
We prove that the best so far known constant of a domination inequality, which originates to Lenglart, is sharp. In particular, we solve an open question posed by Revuz and Yor [12]. Motivated by the application to maximal inequalities, like e.g. the Burkholder-Davis-Gundy inequality, we also study the domination inequality under an additional monotonicity assumption. In this special case, a constant which stays bounded for p near 1 was proven by Pratelli and Lenglart. We provide the sharp constant for this case.
Funding Statement
S. Geiss was supported by the Elsa-Neumann-Stipendium des Landes Berlin.
Citation
Sarah Geiss. Michael Scheutzow. "Sharpness of Lenglart’s domination inequality and a sharp monotone version." Electron. Commun. Probab. 26 1 - 8, 2021. https://doi.org/10.1214/21-ECP413
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