Before revision:  The expansion is performed around the small-variance limit of the forward SDE and does not necessarily require a small size of the non-linearity in the BSDE's driver, which was actually the case for the linearization method proposed by the current authors before in a Brownian setup  .
After revision:  The expansion is performed around the small-variance limit of the forward SDE and does not necessarily require a small size of the non-linearity in the BSDE's driver, which was actually the case for the linearization method proposed by the current authors in a Brownian setup .