Before revision:  In contrast to the naive implementation of marked branching diffusion, the number of branches as well as interactions are efficiently suppressed by the properties of the perturbative expansion. This property will make the numerical implementation more feasible and stable. Furthermore, there is no need of direct approximation of the non-linear driver by a polynomial function .
After revision:  The number of branching points are capped by the order of perturbation, which is expected to make the scheme less numerically intensive .