= Rough differential equation
{title2=$dY=V(Y)\,d\mathbf X$}
A rough differential equation interprets a differential equation using the higher-order data of its driving <rough path>. For $2<p<3$, its local expansion includes $V_i(Y_s)X^i_{s,t}+DV_j(Y_s)V_i(Y_s)\mathbb X^{ij}_{s,t}$, with a remainder controlled at order greater than one. For a smooth driver it is the usual controlled <ordinary differential equation>; for <enhanced Brownian motion> it is the corresponding Stratonovich equation.
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