\frac{1}{4}, \frac{1}{3} \right]$.

The purpose of the present paper is to extend the correction formula to these less regular cases. To do so we will assume that the Gaussian process $X$ is a Volterra process; that is, the covariance function $R$ of each component can be written as $$\begin{aligned}
R(s,t)=\int_{0}^{t\wedge s}K(t,r)K(s,r)\,\mathrm{d}r,\end{aligned}$$ for some kernel $K$, a square-integrable function $K: \left[ 0, T \right]^2  \rightarrow\mathbb{R}$ with $K(t,s)=0,\;\forall s\geq t.$ We will present conditions on $K$ that allow us to generalize . In doing so, we need to overcome a number of serious obstacles. We highlight here the three most salient of these, outline the contribution of the present work and, at the same time, provide a road-map for the paper:

(i) We need to prove that the solution $Y$ belongs to the domain of the Skorohod integral $\delta^{X}.$ In fact we prove the stronger statement that $Y$ belongs to the Malliavin Sobolev space $\mathbb{D}^{1,2} \left(\mathcal{H}_{1} \right) \subset \mathrm{Dom}(\delta^{X})$ (for definitions see Section \[MDsection\]). To show that $Y$, a path-valued random variable, can be understood as a random variable in the Hilbert space $\mathcal{H}_{1}$, we need to identify a class of functions with a subset of $\mathcal{H}_{1}$. This was proved in [@cl2018], 