Improvement of multidimensional randomized Monte Carlo algorithms with “splitting”

Randomized Monte Carlo algorithms are constructed by jointly realizing a baseline probabilistic model of the problem and its random parameters (random medium) in order to study a parametric distribution of linear functionals. This work relies on statistical kernel estimation of the multidimensional distribution density with a “homogeneous” kernel and on a splitting method, according to which a certain number $n$ of baseline trajectories are modeled for each medium realization. The optimal value of $n$ is estimated using a criterion for computational complexity formulated in this work. Analytical estimates of the corresponding computational efficiency are obtained with the help of rather complicated calculations.