Elsevier

Journal of Complexity

Volume 54, October 2019, 101399
Journal of Complexity

Approximation complexity of sums of random processes

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Abstract

We study approximation properties of additive random fields Yd(t),t[0,1]d, dN, which are sums of d uncorrelated zero-mean random processes with continuous covariance functions. 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. The results are applied to the sums of the Wiener processes with different variance parameters.

Keywords

Additive random fields
Average case approximation complexity
Asymptotic analysis
Wiener process

Cited by (0)

Communicated by E. Novak.