L. Plaskota, K. Ritter, and G.W. Wasilkowski

Average case complexity of weighted integration over $R^d$ with isotropic weight

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Abstract.   We study the average case complexity of approximating functions or their integrals over $R^d$. Approximations (quadratures) are constructed based on finitely many function values. We consider these problems in a weighted sense, and we focus on how the complexity depends on the prior distribution and the weight. For the approximation problem, the proofs are constructive. For integration, general upper bounds are obtained by using Monte Carlo arguments.

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