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Approximation complexity of sums of random processes. / Khartov, A.A.; Zani, M.

In: Journal of Complexity, Vol. 54, 101399, 10.2019.

Research output: Contribution to journal › Article › peer-review

Harvard

Khartov, AA & Zani, M 2019, 'Approximation complexity of sums of random processes', Journal of Complexity, vol. 54, 101399. https://doi.org/10.1016/j.jco.2019.02.002

APA

Khartov, A. A., & Zani, M. (2019). Approximation complexity of sums of random processes. Journal of Complexity, 54, [101399]. https://doi.org/10.1016/j.jco.2019.02.002

Vancouver

Khartov AA, Zani M. Approximation complexity of sums of random processes. Journal of Complexity. 2019 Oct;54. 101399. https://doi.org/10.1016/j.jco.2019.02.002

Author

Khartov, A.A. ; Zani, M. / Approximation complexity of sums of random processes. In: Journal of Complexity. 2019 ; Vol. 54.

BibTeX

@article{17e339fc69ed4ae0961b8d1e592630d2,
title = "Approximation complexity of sums of random processes",
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. ",
keywords = "Additive random fields, Asymptotic analysis, Average case approximation complexity, Wiener process",
author = "A.A. Khartov and M. Zani",
year = "2019",
month = oct,
doi = "10.1016/j.jco.2019.02.002",
language = "English",
volume = "54",
journal = "Journal of Complexity",
issn = "0885-064X",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Approximation complexity of sums of random processes

AU - Khartov, A.A.

AU - Zani, M.

PY - 2019/10

Y1 - 2019/10

N2 - 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.

AB - 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.

KW - Additive random fields

KW - Asymptotic analysis

KW - Average case approximation complexity

KW - Wiener process

UR - http://www.scopus.com/inward/record.url?scp=85062453442&partnerID=8YFLogxK

U2 - 10.1016/j.jco.2019.02.002

DO - 10.1016/j.jco.2019.02.002

M3 - Article

VL - 54

JO - Journal of Complexity

JF - Journal of Complexity

SN - 0885-064X

M1 - 101399

ER -

ID: 42683137