  We quantize a multidimensional $SDE$ (in the Stratonovich sense) by solving
the related system of $ODE$'s in which the $d$-dimensional Brownian motion has
been replaced by the components of functional stationary quantizers. We make a
connection with rough path theory to show that the solutions of the quantized
solutions of the $ODE$ converge toward the solution of the $SDE$. On our way to
this result we provide convergence rates of optimal quantizations toward the
Brownian motion for $\frac 1q$-H\" older distance, $q>2$, in $L^p(\P)$.
