= Rough path translation
{title2=$T_h\mathbf X$}
For $2<p<3$ and a continuous path $h$ of <bounded variation>, translate the first level by $h$ and add the mixed integrals $\int X_{s,r}\otimes dh_r$, $\int h_{s,r}\otimes dX_r$ and $\int h_{s,r}\otimes dh_r$ to the second level. <Integration by parts> defines the second mixed integral. The operation is continuous in the <rough path metric> and the variation norm of $h$. For canonical lifts it is precisely the enhancement of the sum of the paths.
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