Tractability of multi-parametric Euler and Wiener integrated processes

Abstrakt

We study average case approximation of Euler and Wiener integrated processes of d variables which are almost surely rk-imes continuously differentiable with respect to the k-th variable and 0 ￢ rk ￢ rk+1. Let n"; 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 ". We prove that the Wiener process is much more difficult to approximate than the Euler process.