×

zbMATH — the first resource for mathematics

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.

MSC:
60J45 Probabilistic potential theory
60J60 Diffusion processes
65C05 Monte Carlo methods
PDF BibTeX XML Cite