Modification of two-step Monte Carlo algorithms based on the symmetry of the first step

Two-step Monte Carlo algorithms are modified taking into account the symmetry (i.e., invariance) of the first step about some initial vector parameter of the modeled trajectory. In the modification, the modeling of this parameter is formally transferred to the second step of the algorithm. In the “splitting method,” this means the randomization of the initial points of auxiliary trajectories. It is shown that the randomization can be improved by applying the Bellman principle.