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 $H\in(1/3,1/2)$, initiated in a paper of Bardina et al. . 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 $B$.
"Weak approximation of fractional SDEs: the Donsker setting." Electron. Commun. Probab. 15 314 - 329, 2010. https://doi.org/10.1214/ECP.v15-1561