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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60H15 Stochastic partial differential equations [See also 35R60]
- 65C30 Stochastic differential and integral equations
- 35R60 Partial differential equations with randomness [See also 60H15]
- 65M06 Finite difference methods

**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)