On geometrical splitting in nonanalog Monte Carlo

A very general geometrical procedure is considered, and it is shown how the free flights, the statistical weights and the contribution of particles participating in splitting are to be chosen in order to reach unbiased estimates in games where the transition kernels are nonanalog. Equations governing the second moment of the score and the number of flights to be stimulated are derived. It is shown that the post-splitting weights of the fragments are to be chosen equal to reach maximum gain in variance. Conditions are derived under which the expected number of flights remains finite. Simplified example illustrate the optimization of the procedure (author)