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Given a solution $Y$ to a rough differential equation (RDE), a recent result[8] extends the classical It\"{o}-Stratonovich formula and provides aclosed-form expression for $\int Y \circ \mathrm{d} \mathbf{X} - \int Y \,\mathrm{d} X$, i.e. the difference between the rough and Skorohod integrals of$Y$ with respect to $X$, where $X$ is a Gaussian process with finite$p$-variation less than 3. In this paper, we extend this result to Gaussianprocesses with finite $p$-variation such that $3 \leq p < 4$. The constraintthis time is that we restrict ourselves to Volterra Gaussian processes withkernels satisfying a natural condition, which however still allows the resultto encompass many standard examples, including fractional Brownian motion with$H > \frac{1}{4}$. Analogously to [8], we first show that the Riemann-sumapproximants of the Skorohod integral converge in $L^2(\Omega)$ by adopting asuitable characterization of the Cameron-Martin norm, before appending theapproximants with higher-level compensation terms without altering the limit.Lastly, the formula is obtained after a re-balancing of terms, and we also showhow to recover the standard It\"{o} formulas in the case where the vectorfields of the RDE governing $Y$ are commutative.

A Stratonovich-Skorohod integral formula for Volterra Gaussian rough paths