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We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0,1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutionsof linear parabolic stochastic partial differential equations on boundedLipschitz domains O\subset R^d. The Besov smoothness determines the order ofconvergence that can be achieved by nonlinear approximation schemes. The proofsare based on a combination of weighted Sobolev estimates and characterizationsof Besov spaces by wavelet expansions.

Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains