Geodesic
On stochastic algorithms for solving boundary value problems for the Laplace operator
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 23, Tome 442 (2015), pp. 133-142 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper deals with the mixed boundary value problem for the Poisson equation. A random walk inside the domain are constructed and unbiased estimator for the solution of the boundary value problem defined on its trajectories. The finiteness of the estimator variance proved. The possibility of practical realization of the estimator by Monte Carlo method studied. 
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     author = {A. S. Sipin},
     title = {On stochastic algorithms for solving boundary value problems for the {Laplace} operator},
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     year = {2015},
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A. S. Sipin. On stochastic algorithms for solving boundary value problems for the Laplace operator. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 23, Tome 442 (2015), pp. 133-142. http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a8/

[1] S. M. Ermakov, A. S. Sipin, Metod Monte-Karlo i parametricheskaya razdelimost algoritmov, S.-Peterburg, SPbGU, 2014

[2] K. K. Sabelfeld, Metody Monte-Karlo v kraevykh zadachakh, Nauka, Novosibirsk, 1989 | MR

[3] S. M. Ermakov, V. V. Nekrutkin, A. S. Sipin, Random Processes for Classical Equations of Mathematical Physics, Kluwer Academic Publishers, Dordrecht, 1989 | MR | Zbl