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The Burkholder-Davis-Gundy Inequality for Enhanced Martingales

Peter Friz·Nicolas Victoir
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Abstract

Multi-dimensional continuous local martingales, enhanced with their stochastic area process, give rise to geometric rough paths with a.s. finite homogenous p-variation, p>2. Here we go one step further and establish quantitative bounds of the p-variation norm in the form of a BDG inequality. Our proofs are based on old ideas by Lepingle. We also discuss geodesic and piecewise linear approximations.

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Peter Friz, Nicolas Victoir. 2006-08-31. The Burkholder-Davis-Gundy Inequality for Enhanced Martingales. https://arxiv.org/abs/math/0608783

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