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

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 $L^p(\mathrm{\Omega };L^2(D))$–norm, for some values of $p$.