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

Teresa Martínez; Marta Sanz-Solé

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

Teresa Martínez·Marta Sanz-Solé

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Abstract

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 $L^p(Ω;L^{2}(D))$--norm, for some values of $p$.

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Teresa Martínez, Marta Sanz-Solé. 2005-08-18. A lattice scheme for stochastic partial differential equations of elliptic type in dimension $d\ge 4$. https://arxiv.org/abs/math/0508339

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