Weak approximation of a fractional SDE

In this note, a diffusion approximation result is shown for stochastic differential equations driven by a (Liouville) fractional Brownian motion B with Hurst parameter H ∈ ( 1 / 3 , 1 / 2 ) . More precisely, we resort to the Kac–Stroock type approximation using a Poisson process studied in Bardina et al. (2003) [4] and Delgado and Jolis (2000) [9], and our method of proof relies on the algebraic integration theory introduced by Gubinelli in Gubinelli (2004) [14].