The Burkholder-Davis-Gundy Inequality for Enhanced Martingales
Peter Friz, Nicolas Victoir
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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