Open Access
2008 Sharp inequality for bounded submartingales and their differential subordinates
Adam Osekowski
Author Affiliations +
Electron. Commun. Probab. 13: 660-675 (2008). DOI: 10.1214/ECP.v13-1433


Let $\alpha$ be a fixed number from the interval $[0,1]$. We obtain the sharp probability bounds for the maximal function of the process which is $\alpha$-differentially subordinate to a bounded submartingale. This generalizes the previous results of Burkholder and Hammack.


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Adam Osekowski. "Sharp inequality for bounded submartingales and their differential subordinates." Electron. Commun. Probab. 13 660 - 675, 2008.


Accepted: 19 December 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1196.60074
MathSciNet: MR2466194
Digital Object Identifier: 10.1214/ECP.v13-1433

Primary: 60G42
Secondary: 60G46

Keywords: conditional differential subordination , Differential subordination , distribution function , martingale , submartingale , tail inequality

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