Average errors for zero finding: lower bounds for smooth or monotone functions. (Summary).
We use the scale of Besov spaces , 1/τ = α/d + 1/p, α > 0, p fixed, to study the spatial regularity of solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains ⊂ ℝ. The Besov smoothness determines the order of convergence that can be achieved by nonlinear approximation schemes. The proofs are based on a combination of weighted Sobolev estimates and characterizations of Besov spaces by wavelet expansions.
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