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abstract:
We study the spatial regularity of the solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains D\subset\R^d within the scale of Besov spaces B^\alpha_{\tau,\tau}(D), \alpha>0, 1/\tau=\alpha/d+1/p, where p\geq2 . Results on weighted Sobolev norms of the solutions are combined with methods from wavelet analysis. The smoothness in the considered scale of Besov spaces determines the order of convergence that can be achieved by nonlinear approximation. |
