# Stability and genericity for SPDEs driven by spatially correlated noise

Abstract : We consider stochastic partial differential equations on $\mathbb{R}^{d}, d\geq 1$, driven by a Gaussian noise white in time and colored in space, for which the pathwise uniqueness holds. By using the Skorokhod representation theorem we establish various strong stability results. Then, we give an application to the convergence of the Picard successive approximation. Finally, we show that in the sense of Baire category, almost all stochastic partial differential equations with continuous and bounded coefficients have the properties of existence and uniqueness of solutions as well as the continuous dependence on the coefficients.
Type de document :
Article dans une revue
Journal of Mathematics of Kyoto University, 2008, 48 (4), pp.699-724
Domaine :

https://hal.archives-ouvertes.fr/hal-00325073
Contributeur : Mohamed Mellouk <>
Soumis le : vendredi 26 septembre 2008 - 10:44:57
Dernière modification le : mardi 11 octobre 2016 - 11:58:20

### Citation

K. Bahlali, M. Eddahbi, Mohamed Mellouk. Stability and genericity for SPDEs driven by spatially correlated noise. Journal of Mathematics of Kyoto University, 2008, 48 (4), pp.699-724. <hal-00325073>

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