V^2(Y_{t_{i}^{n}}) \left( \mathbf{X}_{t_{i}^{n},t_{i+1}^{n}}^{3}\right),\end{aligned}$$ possibly after rebalancing, over a sequence of partitions with mesh tending to zero. An important discovery of this paper is the somewhat surprising conclusion that this these terms have vanishing $L^{2}(\Omega)-$limit, without the the need to subtract any rebalancing terms. This is the concluding result of Section \[Sko aug\].

(iii) The proof of point (ii) relies on a rather intricate interplay between estimates from Malliavin’s calculus and rough path analysis. From the latter theory, we need estimates on the directional derivatives of RDE solutions. It is well known that an RDE solution of the form can be differentiated in a direction $h\in C^{q-\text{var}}\left(  \left[  0,T\right], \mathbb{R}^{d}\right)$ by considering the perturbed RDE solution driven by the translated rough path $T_{\epsilon h}\mathbf{X}$ and then evaluating the derivative in $\epsilon$ at zero. For $T_{\epsilon h}\mathbf{X}$ to make sense, $\mathbf{X}$ and $h$ must have Young-complementary regularity, i.e. $\frac{1}{p} + \frac{1}{q} > 1$, in which case Duhamel’s formula gives $$\begin{aligned}
     \label{first o}
    D_{g}Y_{t}=\int_{0}^{t}J_{t}^{\mathbf{X}}\left(  J_{s}^{\mathbf{X}}\right)^{-1}V\left(  Y_{s}\right)  \,\mathrm{d}g(s),\end{aligned}$$ a well-defined Young integral. In Malliavin calculus, $g$ will typically be an element of the Cameron-Martin space (written as $\mathcal{H}^{d}$ in this paper), and this has spurred interest in results that prove that $\mathcal{H}^{d}$ can be 