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

Problems of the accuracy of statistical simulation algorithms are investigated for boundary-value problems of mathematical physics for the elliptic equations. These algorithms are based on a probabilistic representation of these solutions with the use of appropriate systems of the stochastic differential equations. The problems in question are due to the necessity to simulate long SDE trajectories and the estimation of expectation of random variables with asymmetric distribution. Numerical results are given.