Information of varying cardinality
Journal of Complexity
Information-based complexity
Average case L∞ -approximation in the presence of Gaussian noise
Journal of Approximation Theory
Average case complexity of weighted approximation and integration over R+
Journal of Complexity
Randomly shifted lattice rules for unbounded integrands
Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005
Adaptive Itô-Taylor algorithm can optimally approximate the Itô integrals of singular functions
Journal of Computational and Applied Mathematics
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We study minimal errors and optimal designs for weighted L2-approximation and weighted integration of Gaussian stochastic processes X defined on the half-line [0, ∞). Under some regularity conditions, we obtain sharp bounds for the minimal errors for approximation and upper bounds for the minimal errors for integration. The upper bounds are proven constructively for approximation and non-constructively for integration. For integration of the r-fold integrated Brownian motion, the upper bound is proven constructively and we have a matching lower bound.