Tractability of Multi-Parametric Euler and Wiener Integrated Processes

Details Tractability of Multi-Parametric Euler and Wiener Integrated Processes Tractability of Multi-Parametric Euler and Wiener Integrated Processes

2011-12-19

arxiv.org/abs/1112.4248v1

Mathematics

Probability

Scientific paper

We study average case approximation of Euler and Wiener integrated processes of d variables which are almost surely r_k-times continuously differentiable with respect to the k-th variable. Let n(h,d) denote the minimal number of continuous linear functionals which is needed to find an algorithm that uses n such functionals and whose average case error improves the average case error of the zero algorithm by a factor h. Strong polynomial tractability means that there are nonnegative numbers C and p such that n(h,d)< C h^{-p} for all d and 0 1/(2\ln 3), whereas it holds for the Wiener case iff liminf r_k/k^s > 0 for some s>1/2. Other types of tractability are also studied.

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