Monte Carlo approximations of the Neumann problem

@article{Maire2013MonteCA,
  title={Monte Carlo approximations of the Neumann problem},
  author={Sylvain Maire and Etienne Tanr{\'e}},
  journal={Monte Carlo Meth. and Appl.},
  year={2013},
  volume={19},
  pages={201-236}
}
We introduce Monte Carlo methods to compute the solution of elliptic equations with pure Neumann boundary conditions. We first prove that the solution obtained by the stochastic representation has a zero mean value with respect to the invariant measure of the stochastic process associated to the equation. Pointwise approximations are computed by means of standard and new simulation schemes especially devised for local time approximation on the boundary of the domain. Global approximations are… CONTINUE READING
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