  In this note, we take up the study of weak convergence for stochastic
differential equations driven by a (Liouville) fractional Brownian motion $B$
with Hurst parameter $H\in(1/3,1/2)$. In the current paper, we approximate the
$d$-dimensional fBm by the convolution of a rescaled random walk with
Liouville's kernel. We then show that the corresponding differential equation
converges in law to a fractional SDE driven by $B$.
