A lattice scheme for stochastic partial differential equations of elliptic type in dimension $d\ge 4$

Details A lattice scheme for stochastic partial differential equations of elliptic type in dimension $d\ge 4$ A lattice scheme for stochastic partial differential equations of elliptic type in dimension $d\ge 4$

2005-08-18

arxiv.org/abs/math/0508339v1

Mathematics

Probability

27 pages

Scientific paper

We study a stochastic boundary value problem on $(0,1)^d$ of elliptic type in
dimension $d\ge 4$, driven by a coloured noise. An approximation scheme based
on a suitable discretization of the Laplacian on a lattice of $(0,1)^d$ is
presented; we also give the rate of convergence to the original SPDE in
$L^p(\Omega;L^{2}(D))$--norm, for some values of $p$.

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