Average case tractability of a multivariate approximation problem

Abstract

Many authors have studied exponentially-convergent tractability (EC-tractability) in the worst case setting. Here, we study EC-tractability in the average case setting. Our problem is multivariate approximation over the space of continuous real functions equipped with a zero-mean Gaussian measure whose covariance kernel is given as a Korobov kernel. We obtain necessary and sufficient conditions for certain kinds of tractability, includingEC-tractability.