Before revision:  In the case of a finite jump measure with a bounded intensity, the method can also handle sate-dependent ( and hence non-Poissonian ) jumps, which are quite relevant for many practical applications . Based on the stability result, we also provide a rigorous justification to use arbitrarily smooth coefficients in FBSDEs for any approximation purpose whenever rather mild conditions are satisfied .
After revision:  In the case of a finite jump measure with a bounded intensity, the method can also handle sate-dependent ( and hence non-Poissonian jumps, which are quite relevant for many practical applications . Based on the stability result, we also provide a rigorous justification to use arbitrarily smooth coefficients in FBSDEs for any approximation purpose whenever rather mild conditions are satisfied .