Solving Dirichlet problems numerically using the Feynman-Kac representation
The authors consider the numerical solutions of the Dirichlet problem in high dimensions. By exploiting the Feynman-Kac formula Monte Carlo simulations of the underlying solutions of stochastic differential equations are performed. This involves the approximation of exit times and process values at the boundary. The walk on cubes method is studied and comparisons are made with Milstein's walk on spheres.
scientific article; zbMATH DE number 2073448