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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.

60J45 Probabilistic potential theory
60J60 Diffusion processes
65C05 Monte Carlo methods