ON STOCHASTIC ALGORITHMS FOR SOLVING BOUNDARY-VALUE PROBLEMS FOR THE LAPLACE OPERATOR

摘要

The paper deals with the mixed boundary-value problem for the Poisson equation. Random walks inside the domain are constructed and unbiased estimators for the solution of the boundary-value problem are defined on their trajectories. The finiteness of the estimator variance is proved. The possibility of practical realization of the estimators by the Monte Carlo method is studied. Bibliography: 3 titles.