The “walk in hemispheres” process and its applications to solving boundary value problems

S. M. Ermakov, Monte Carlo Methods in Computational Mathematics: An Introductory Course (St. Petersburg, 2009).

S. M. Ermakov and G. A. Mikhailov, A Course in Statistical Modeling (Nauka, Moscow, 1976) [in Russian].

M. E. Muller, “Some Continuous Monte Carlo Methods for the Dirichlet Problem,” Ann. Math. Stat. 27(3), 569–589 (1956).

A. S. Sipin, “Solving First Boundary Value Problem for Elliptic Equation by Monte Carlo Method,” in Monte Carlo Methods in Comput. Math. and Math. Phys. (Novosibirsk, 1979), vol. 2, 113–119.

S. M. Ermakov, V. V. Nekrutkin, and A. S. Sipin, Random Processes for Classical Equations of Mathematical Physics (Nauka, Moscow, 1984; Kluwer, Dordrecht, 1989).

V. S. Vladimirov, Equations of Mathematical Physics (Nauka, Moscow, 1981; Marcel Dekker, New York, 1971).

G. A. Mikhailov, Weighted Algorithms for the Statistical Modeling (Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, 2003) [in Russian].

E. B. Dynkin and A. A. Yushkevich, Markov Processes—Theorems and Problems (Nauka, Moscow, 1967; Plenum, New York, 1969).

P. A. Meyer, Probability and Potentials (Blaisdell, New York, 1966; Mir, Moscow, 1973).

A. S. Sipin, “Walks inside Domains and Their Applications to Boundary Value Problems,” Proc. Conf. “Tikhonov and Contemporary Mathematics”, subsection “Computat. Math. and Informatics”. Moscow, 2006, 113–114.

N. A. Simonov, “Monte Carlo Methods for Solving Elliptic Equations with Boundary Conditions Containing the Normal Derivative,” Doklady Mathematics 74(2), 656–659 (2006).

N. A. Simonov, “Algorithms of Random Walks in Spheres for Solving Mixed Boundary Value Problem and the Neumann Problem,” Siberian J. Comput. Math 10(2), 209–220 (2007).