Mathematics > Probability
[Submitted on 24 May 2007]
Title:Burkholder's submartingales from a stochastic calculus perspective
View PDFAbstract: We provide a simple proof, as well as several generalizations, of a recent result by Davis and Suh, characterizing a class of continuous submartingales and supermartingales that can be expressed in terms of a squared Brownian motion and of some appropriate powers of its maximum. Our techniques involve elementary stochastic calculus, as well as the Doob-Meyer decomposition of continuous submartingales. These results can be used to obtain an explicit expression of the constants appearing in the Burkholder-Davis-Gundy inequalities. A connection with some balayage formulae is also established.
Submission history
From: Giovanni Peccati [view email] [via CCSD proxy][v1] Thu, 24 May 2007 18:05:00 UTC (9 KB)
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