On Stochastic Algorithms for Solving Boundary-Value Problems for the Laplace Operator

Аннотация

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.