### 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 language | English |
---|---|

Article number | 101399 |

Journal | Journal of Complexity |

Volume | 54 |

Early online date | 28 Feb 2019 |

DOIs | |

Publication status | Published - 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

### Cite this

*Journal of Complexity*,

*54*, [101399]. https://doi.org/10.1016/j.jco.2019.02.002