1. Philipps-Universit?t Marburg, Marburg, Germany 4. TU Kaiserslautern, Kaiserslautern, Germany 2. TU Dresden, Dresden, Germany 3. Johannes Gutenberg-Universit?t Mainz, Mainz, Germany
Abstract:
We study the Besov regularity as well as linear and nonlinear approximation of random functions on bounded Lipschitz domains in ?d. The random functions are given either (i) explicitly in terms of a wavelet expansion or (ii) as the solution of a Poisson equation with a right-hand side in terms of a wavelet expansion. In the case (ii) we derive an adaptive wavelet algorithm that achieves the nonlinear approximation rate at a computational cost that is proportional to the degrees of freedom. These results are matched by computational experiments.