A lattice scheme for stochastic partial differential equations of elliptic type in dimension d≥ 4

2005/08/18 by Teresa Martínez, Teresa Martı́nez, Martínez, Teresa +3
Computer Science · Economics, Econometrics and Finance · Mathematics · #35J05 #60H15 #60H35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #math.AP #math.PR #msc:35J05 #msc:60H15 #msc:60H35

paper · pdf · doi:10.48550/arxiv.math/0508339

27 pages

arxiv created 2005/08/18 · openalex publication_date 2005/08/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a stochastic boundary value problem on (0,1)^d of elliptic type in dimension d≥ 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;L²(D))--norm, for some values of p.

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