The Burkholder-Davis-Gundy Inequality for Enhanced Martingales
Probability
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0608783,
title = {The Burkholder-Davis-Gundy Inequality for Enhanced Martingales},
author = {Peter Friz and Nicolas Victoir},
journal= {arXiv preprint arXiv:math/0608783},
year = {2007}
}