Approximation complexity of sums of random processes

A.A. Khartov, M. Zani

Research output


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 (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 the sums of the Wiener processes with different variance parameters.

Original languageEnglish
Article number101399
JournalJournal of Complexity
Early online date28 Feb 2019
Publication statusPublished - Oct 2019


Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • Mathematics(all)
  • Control and Optimization
  • Applied Mathematics

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