Approximation complexity of sums of random processes

Abstract We study approximation properties of additive random fields Y d ( t ) , t ∈ [ 0 , 1 ] d , d ∈ N , which are sums of d uncorrelated zero-mean random processes with continuous covariance functions. The average case approximation complexity n Y d ( e ) 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 e ∈ ( 0 , 1 ) . We investigate the growth of n Y d ( e ) for arbitrary fixed e ∈ ( 0 , 1 ) and d → ∞ . The results are applied to the sums of the Wiener processes with different variance parameters.