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Article Dans Une Revue Journal of Mathematics of Kyoto University Année : 2008

Stability and genericity for SPDEs driven by spatially correlated noise

Résumé

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.

Dates et versions

hal-00325073 , version 1 (26-09-2008)

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Khaled 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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