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Interpretation of a Monte Carlo approach of a finite difference scheme by a game method for modelling. (English) Zbl 1325.65011

Summary: A Monte Carlo technique of a finite difference scheme is interpreted by a game method for modelling (GMM). The simple GMM model is approximated by a second-order difference scheme. To estimate the number of moves (jumps) from a given point of the domain to the boundary we approximate the finite difference scheme by a boundary value problem for an elliptic partial differential equation. Then we use the fundamental solution of the problem as an approximation to the avergae number of moves needed to reach the boundary from an arbitrary point inside the domain.

MSC:

65C05 Monte Carlo methods
65N06 Finite difference methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
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