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 ∈ (1/3, 1/2), initiated in . 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. © 2010 Applied Probability Trust.
- Fractional Brownian motion
- Kac-Stroock type approximation
- Rough paths
- Weak approximation