Approximation complexity of homogeneous sums of random processes

2018/05/31 by A. A. Khartov, Khartov, A. A., Marguerite Zani +2
Mathematics · #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Statistical Methods and Inference #math.PR #msc:41A25 #msc:41A63 #msc:41A65 #msc:60G60 #msc:65Y20

paper · pdf · doi:10.48550/arxiv.1805.12581

arxiv created 2018/05/31 · arxiv updated 2018/06/01

Abstract

We study approximation properties of additive random fields Y_d, d∈ℕ, which are sums of zero-mean random processes with the same continuous covariance functions. The average case approximation complexity n^Y_d(ε) 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 ε∈(0,1). We investigate the growth of n^Y_d(ε) for arbitrary fixed ε∈(0,1) and d→∞. The results are applied to sums of standard Wiener processes.

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