Interpretation of a Monte Carlo approach of a finite difference scheme by a game method for modelling
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A Monte Carlo technique of a finite difference scheme is interpretedby a game method for modelling (GMM). The simple GMM model isapproximated by a second order difference scheme. To estimate thenumber of moves (jumps) from a given point of the domain to theboundary we approximate the finite difference scheme by a boundaryvalue problem for an elliptic partial differential equation. Then weuse the fundamental solution of the problem as an approximation tothe average number of moves needed to reach the boundary from anarbitrary point inside the domain.
Abstract
A Monte Carlo technique of a finite difference scheme is interpretedby a game method for modelling (GMM). The simple GMM model isapproximated by a second order difference scheme. To estimate thenumber of moves (jumps) from a given point of the domain to theboundary we approximate the finite difference scheme by a boundaryvalue problem for an elliptic partial differential equation. Then weuse the fundamental solution of the problem as an approximation tothe average number of moves needed to reach the boundary from anarbitrary point inside the domain.
참고문헌 (2)
- K. T. Atanassov, "On the game method for modelling", Advanced Studies in Contemporary Mathematics, 22(2), pp.189~207 (2012), 장전수학회
- Dimov, I., "Monte Carlo Methods for Applied Scientists", pp.291~, World Scientific