Asymptotic analysis of average case approximation complexity of additive random fields

Abstract

We study approximation properties of centred additive random fields Yd, d∈N. The average case approximation complexity nYd(ε) is defined as the minimal number of evaluations of arbitrary linear functionals needed to approximate Yd, with relative 2-average error not exceeding a given threshold ε∈(0,1). We investigate the growth of nYd(ε) for arbitrary fixed ε∈(0,1) and d→∞. Under natural assumptions we obtain general results concerning asymptotics of nYd(ε). We apply our results to additive random fields with marginal random processes corresponding to the Korobov kernels.