Average case [formula omitted]-weak tractability of non-homogeneous tensor product problems

Abstract

We study d-variate problems in the average case setting with respect to a zero-mean Gaussian measure. The covariance kernel of this Gaussian measure is a product of univariate kernels and satisfies some special properties. We study (s,t)-weak tractability of this multivariate problem under the absolute or normalized error criterion, and obtain a necessary and sufficient condition for s>0 and t∈(0,1). Our result can apply to the problems with covariance kernels corresponding to Euler and Wiener integrated processes, Korobov kernels, and analytic Korobov kernels.