Mil’shtejn, G. N.; Rybkina, N. F. An algorithm for random walks over small ellipsoids for solving the general Dirichlet problem. (English. Russian original) Zbl 0795.60073 Comput. Math. Math. Phys. 33, No. 5, 631-647 (1993); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 5, 704-725 (1993). Summary: To solve the general Dirichlet problem, the usual probability representation in the form of the mathematical expectation of a functional which depends on paths of a definite system of stochastic differential equations is replaced by a realizable probability representation which depends on approximate discrete paths. The coefficients of the equation are frozen and then the next point on the path is found by a random walk over the boundary of a small ellipsoid with centre at the previous point. The convergence of the proposed algorithm is investigated. Cited in 2 Documents MSC: 60J45 Probabilistic potential theory 60J60 Diffusion processes 65C05 Monte Carlo methods Keywords:Dirichlet problem; stochastic differential equations; random walk PDF BibTeX XML Cite \textit{G. N. Mil'shtejn} and \textit{N. F. Rybkina}, Comput. Math. Math. Phys. 33, No. 5, 704--725 (1993; Zbl 0795.60073); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 5, 704--725 (1993)