  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.
