Zero-Variance Monte Carlo Schemes Revisited

Zero-variance Monte Carlo schemes have been discussed in the literature at several places. Taking a fresh look, it turns out that some authors made essential errors in their derivation and conclusions. We will prove that for a given estimator there is only one zero-variance scheme possible with a unique biasing of the source function and the transition and collision kernels. A practical demonstration of a zero-variance scheme will be shown numerically for a two-group homogeneous slab system treated by the two-direction transport model, which provides an analytical solution for the particle flux and adjoint functions.