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Fall 2008 Burkholder’s submartingales from a stochastic calculus perspective
Giovanni Peccati, Marc Yor
Illinois J. Math. 52(3): 815-824 (Fall 2008). DOI: 10.1215/ijm/1254403716

Abstract

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.

Citation

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Giovanni Peccati. Marc Yor. "Burkholder’s submartingales from a stochastic calculus perspective." Illinois J. Math. 52 (3) 815 - 824, Fall 2008. https://doi.org/10.1215/ijm/1254403716

Information

Published: Fall 2008
First available in Project Euclid: 1 October 2009

zbMATH: 1176.60033
MathSciNet: MR2546009
Digital Object Identifier: 10.1215/ijm/1254403716

Subjects:
Primary: 60G15, 60G44

Rights: Copyright © 2008 University of Illinois at Urbana-Champaign

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Vol.52 • No. 3 • Fall 2008
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