Approximation complexity of sums of random processes

A.A. Khartov, M. Zani

Research output

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 (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
Volume54
Early online date28 Feb 2019
DOIs
Publication statusPublished - Oct 2019

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Scopus subject areas

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

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