On implicit and explicit discretization schemes for parabolic SPDEs in any dimension

Annie Millet (1, 2, 3) , Pierre-Luc Morien (4)

1 SAMOS - Statistique Appliquée et MOdélisation Stochastique
2 MATISSE - UMR 8595 - Modélisation Appliquée, Trajectoires Institutionnelles et Stratégies Socio-Économiques
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
4 MODAL'X - Modélisation aléatoire de Paris X

We study the speed of convergence of the explicit and implicit space-time discretization schemes of the solution $u(t,x)$ to a parabolic partial differential equation in any dimension perturbed by a space-correlated Gaussian noise. The coefficients only depend on $u(t,x)$ and the influence of the correlation on the speed is observed.

Mots clés: Parabolic SPDE; Implicit and explicit space-time discretization schemes; Green function; Gaussian noise; Space correlation; Speed of convergence; Numerical simulations

Domaines: Probabilités [math.PR]

Annie Millet, Pierre-Luc Morien. On implicit and explicit discretization schemes for parabolic SPDEs in any dimension. Stochastic Processes and their Applications, 2005, 115, pp.1073-1106. ⟨10.1016/j.spa.2005.02.004⟩. ⟨hal-00111094⟩