Study of weighted Monte Carlo algorithms with branching

Various weighted algorithms for numerical statistical simulation are formulated and studied. The trajectory of an algorithm branches when the current weighting factor exceeds unity. As a result, the weight of an individual branch does not exceed unity and the variance of the estimate for the computed functional is finite. The unbiasedness and finiteness of the variance of estimates are analyzed using the recurrence “partial“ averaging method formulated in this study. The estimation of the particle reproduction factor and solutions to the Helmholtz equation are considered as applications. The comparative complexity of the algorithms is examined using a test problem. The variances of weighted algorithms with branching as applied to integral equations with power nonlinearity are analyzed.