On Some Stochastic Algorithms for the Numerical Solution of the First Boundary Value Problem for the Heat Equation

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We deal with statistical modeling algorithms for the numerical solution of the first boundary value problem for the heat equation. Unbiased estimators of the solution of a boundary value problem are built on the trajectories of random walks. We consider a random walk on the boundary and a random walk on the cylinders inside the region in which the boundary problem must be solved. The results of computational experiments and some applications are presented. The complexity of algorithms are estimated numerically.