Approximation complexity of sums of random processes

We study approximation properties of additive random fields Y-d(t), t is an element of[0, 1](d), d is an element of N, which are sums of d uncorrelated zero mean random processes with continuous covariance functions. The average case approximation complexity n(Yd)(epsilon) is defined as the minimal number of evaluations of arbitrary linear functionals needed to approximate Y-d, with relative 2-average error not exceeding a given threshold epsilon is an element of(0, 1). We investigate the growth of n(Yd)(epsilon) for arbitrary fixed epsilon is an element of(0, 1) and d -> infinity. The results are applied to the sums of the Wiener processes with different variance parameters. (C) 2019 Elsevier Inc. All rights reserved.