Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

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

Auteur(s):

Code(s) de Classification MSC:

Résumé: 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; in the limit case, corresponding to the space-time white noise in dimension 1, we recover the speeds obtained by I. Gyöngy.

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

Date: 2003-05-20

Prépublication numéro: PMA-821

Revised version : PMA-821bis.pdf. (January 11 2005)