Analysis of the accuracy of Monte Carlo methods for boundary-value problems using a probabilistic representation

Accuracy problems for statistical simulation algorithms are explored in solving boundary-value problems for elliptic equations in mathematical physics. The algorithms are based on a probabilistic representation of the solutions with the use of appropriate systems of stochastic differential equations (SDEs). The problems in question arise from the necessity to simulate long SDE trajectories and estimate expectations of random variables with strongly asymmetric distributions. Numerical results are presented.