References
M. E. Muller, “Some continuous Monte Carlo methods for the Dirichlet problem,” Ann. Math. Statist.,27, No. 3, 569–589 (1956).
B. S. Elepov and G. A. Mikhaîlov, “Algorithms of a ‘random walk by spheres’ for the equation Δu−cu=−g,” Dokl. Akad. Nauk SSSR,212, No. 1, 15–18 (1973).
S. M. Ermakov, V. V. Nekrutkin, and A. S. Sipin, Stochastic Processes for Solving Classical Equations of Mathematical Physics [in Russian], Nauka, Moscow (1984).
G. A. Mikhaîlov, “New Monte Carlo methods for solving the Helmholtz equation,” Dokl. Akad. Nauk,326, No. 6, 943–947 (1992).
G. A. Mikhailov, New Monte Carlo Methods with Estimating Derivatives, VSP, Utrecht and Tokyo (1995).
S. M. Ermakov and G. A. Mikhaîlov, Statistical Modeling [in Russian], Nauka, Moscow (1982).
B. C. Elepov and G. A. Mikhaîlov, “To the theory of the estimators of the Monte Carlo method which are connected with a ‘random walk by spheres,’” Sibirsk. Mat. Zh.,36, No. 3, 543–550 (1995).
M. Kac, Probability and Related Topics in Physical Sciences [Russian translation], Mir, Moscow (1965).
R. Courant, Partial Differential Equations [Russian translation], Mir, Moscow (1964).
V. Ya. Arsenin, Methods of Mathematical Physics and Special Functions [in Russian], Nauka, Moscow (1974).
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To the 65 Anniversary of Academician A. A. Borovkov.
Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 37, No. 4, pp. 881–888, July–August, 1996.
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Mikhaîlov, G.A., Men'shchikov, B.V. Solving boundary value problems with complex parameters by the Monte Carlo method. Sib Math J 37, 775–781 (1996). https://doi.org/10.1007/BF02104668
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DOI: https://doi.org/10.1007/BF02104668