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 in a Brownian setup before. A semi-analytic solution technique , which only requires a system of ODEs (one is non-linear and the others are linear) to be solved, as well as its error estimate are provided .
After revision:  The expansion is performed around the small-variance limit of the forward SDE . We provide a semi-analytic solution technique , which only requires a system of ODEs (one is non-linear and the others are linear) to be solved, as well as its error estimate are provided .