Solution of some semi-linear Dirichlet problem by Monte Carlo method

In this paper, a Dirichlet boundary value problem (BVR) for semi-linear elliptic equation is considered. Assuming the existence of solution BVR we obtained a probabilistic representation of the solution as a mathematical expectation of some random variable. In accordance with a probabilistic representation were constructed on the trajectories of the branching random process unbiased estimator of the solution. An unbiased estimator of the solution has finite variance, based on the trajectories of a branching process with a finite average number of branchings. Some numerical experiments are performed.

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